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62 lines
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Dreiecklogseq____",536870918]],[logseq____"^15logseq____",[33,logseq____"^Blogseq____",1696963728591,536870918]],[logseq____"^15logseq____",[33,logseq____"^;logseq____",logseq____"~u65259c90-daa6-4800-bfef-89b043f15a22logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Klogseq____",1696963728598,536870918]],[logseq____"^15logseq____",[34,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[34,logseq____"^Ylogseq____",logseq____"rationalmachenlogseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^11logseq____",logseq____"Rationalmachenlogseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Blogseq____",1696963728598,536870918]],[logseq____"^15logseq____",[34,logseq____"^;logseq____",logseq____"~u65259c90-aec0-44d0-a040-9239782d5740logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Klogseq____",1696963728593,536870918]],[logseq____"^15logseq____",[35,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[35,logseq____"^Ylogseq____",logseq____"auffrischung mathe 1logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^11logseq____",logseq____"Auffrischung Mathe 1logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Blogseq____",1696963728593,536870918]],[logseq____"^15logseq____",[35,logseq____"^;logseq____",logseq____"~u65259c90-efaa-4b02-bb3a-402e2f4a2ceflogseq____",536870920]],[logseq____"^15logseq____",[36,logseq____"^Klogseq____",1696963728594,536870918]],[logseq____"^15logseq____",[36,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[36,logseq____"^Ylogseq____",logseq____"fixmelogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^11logseq____",logseq____"FIXMElogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Blogseq____",1696963728594,536870918]],[logseq____"^15logseq____",[36,logseq____"^;logseq____",logseq____"~u65259c91-5f5b-4176-bacf-0cd2720f73eblogseq____",536870921]],[logseq____"^15logseq____",[37,logseq____"^Klogseq____",1696963728603,536870918]],[logseq____"^15logseq____",[37,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[37,logseq____"^Ylogseq____",logseq____"pq-formellogseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^11logseq____",logseq____"pq-Formellogseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Blogseq____",1696963728603,536870918]],[logseq____"^15logseq____",[37,logseq____"^;logseq____",logseq____"~u65259c90-22ed-424c-893c-0635558ef84alogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Klogseq____",1696963728596,536870918]],[logseq____"^15logseq____",[38,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[38,logseq____"^Ylogseq____",logseq____"nennerlogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^11logseq____",logseq____"Nennerlogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Blogseq____",1696963728596,536870918]],[logseq____"^15logseq____",[38,logseq____"^;logseq____",logseq____"~u65259c90-bfe3-43fb-8bfc-4c5c0a56b8eelogseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Qlogseq____",logseq____"$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=(-1)^\\\\frac22logseq____&=(-1)^1logseq____&=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=1^\\\\frac12logseq____&logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Flogseq____",60,536870918]],[logseq____"^15logseq____",[39,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[39,logseq____"^Vlogseq____",46,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[39,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[39,logseq____"^;logseq____",logseq____"~u65259c90-4678-435f-9b3f-c6bbd1bf0c30logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Flogseq____",55,536870918]],[logseq____"^15logseq____",[40,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[40,logseq____"^Vlogseq____",55,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",33,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[40,logseq____"^Hlogseq____",33,536870918]],[logseq____"^15logseq____",[40,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[40,logseq____"^;logseq____",logseq____"~u65259c90-0e38-4f4f-b203-6e839a2b4a24logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Flogseq____",79,536870918]],[logseq____"^15logseq____",[41,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[41,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[41,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[41,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[41,logseq____"^;logseq____",logseq____"~u65259c90-31a9-447b-81b6-bba2d209898clogseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Flogseq____",81,536870918]],[logseq____"^15logseq____",[42,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[42,logseq____"^Vlogseq____",81,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[42,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:headinglogseq____",1],536870918]],[logseq____"^15logseq____",[42,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[42,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[42,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[42,logseq____"^;logseq____",logseq____"~u65259c90-624a-491d-9cc2-5fb461c266cflogseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Qlogseq____",logseq____"logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Flogseq____",73,536870918]],[logseq____"^15logseq____",[43,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[43,logseq____"^Vlogseq____",82,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[43,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[43,logseq____"^;logseq____",logseq____"~u65259c90-af4c-4a1a-8483-8ddbe07307d5logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Flogseq____",45,536870918]],[logseq____"^15logseq____",[44,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[44,logseq____"^Vlogseq____",62,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[44,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[44,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[44,logseq____"^;logseq____",logseq____"~u65259c90-dbea-4150-b40d-6975db55f156logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(2x+y)^4logseq____&=(2x)^4+4*(2x)^3y+6*(2x)^2y^2+4*2xy^3+y^4\\\\notag\\\\\\\\\\nlogseq____&=16x^4+32x^3y+24x^2y^2+8xy^3+y^4\\\\\\\\\\n(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5logseq____&=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Flogseq____",71,536870918]],[logseq____"^15logseq____",[45,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[45,logseq____"^Vlogseq____",62,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[45,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[45,logseq____"^;logseq____",logseq____"~u65259c90-fee7-489d-b68b-cd27ff9f38e9logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Flogseq____",52,536870918]],[logseq____"^15logseq____",[46,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[46,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[46,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[46,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[46,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[46,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[46,logseq____"^;logseq____",logseq____"~u65259c90-3eff-4bca-ab71-41deb6c6874flogseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&= \\\\frac1{\\\\ln a}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Flogseq____",58,536870918]],[logseq____"^15logseq____",[47,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[47,logseq____"^Vlogseq____",52,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[47,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[47,logseq____"^;logseq____",logseq____"~u65259c90-2312-4986-88b3-6a23efe970f7logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Flogseq____",46,536870918]],[logseq____"^15logseq____",[48,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[48,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[48,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[48,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[48,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[48,logseq____"^;logseq____",logseq____"~u65259c90-9354-4f45-b09b-74e6f82441fflogseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&=a^\\\\frac mn\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Flogseq____",74,536870918]],[logseq____"^15logseq____",[49,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[49,logseq____"^Vlogseq____",63,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[49,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[49,logseq____"^;logseq____",logseq____"~u65259c90-81bd-4ef5-ad1d-9673d4c217cblogseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&=a^2-b^2\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Flogseq____",61,536870918]],[logseq____"^15logseq____",[50,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[50,logseq____"^Vlogseq____",42,536870918]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[50,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[50,logseq____"^;logseq____",logseq____"~u65259c90-0098-42c3-ac39-f6e960ff72calogseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Qlogseq____",logseq____"$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Flogseq____",57,536870918]],[logseq____"^15logseq____",[51,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[51,logseq____"^Vlogseq____",57,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",34,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",38,536870918]],[logseq____"^15logseq____",[51,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[51,logseq____"^;logseq____",logseq____"~u65259c90-ad22-4ebe-af32-347be3293a2alogseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Flogseq____",82,536870918]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[52,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[52,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[52,logseq____"^Hlogseq____",27,536870918]],[logseq____"^15logseq____",[52,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u65259c90-9c09-4189-8c13-64bc186eed7dlogseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Qlogseq____",logseq____"$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&\\\\text{plus }logseq____&\\\\text{cubus }logseq____&\\\\text{acq }logseq____&6\\\\\\\\\\nxlogseq____&+logseq____&x^3logseq____&=logseq____&6\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",50,536870918]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",42,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u65259c90-af5a-4ca7-b778-3d4501f6c16elogseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"$\\\\frac12 \\\\sqrt2, \\\\frac12, \\\\frac12\\\\sqrt3 \\\\text{ sind werte von }\\\\sin x$\\n\\\\begin{align}\\n\\\\sin 30\\\\degreelogseq____&=\\\\frac12\\\\\\\\\\n\\\\sin 45\\\\degree logseq____&= \\\\frac12\\\\sqrt2 \\\\\\\\\\n\\\\sin 60\\\\degree logseq____&= \\\\frac12 \\\\sqrt3 \\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",79,536870918]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",79,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u65259c90-5229-4dde-812b-9791ebc439bclogseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",44,536870918]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",62,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[55,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[55,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[55,logseq____"^Hlogseq____",28,536870918]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u65259c90-1b0a-4796-9735-f3ff663db0f4logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"## [[pq-Formel]]logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",75,536870918]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",75,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",37,536870918]],[logseq____"^15logseq____",[56,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[56,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[56,logseq____"^Hlogseq____",37,536870918]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u65259c90-f9c8-426b-a229-56805c302349logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"## [[Rationalmachen]] des [[Nenner]]slogseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",78,536870918]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",63,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",34,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",38,536870918]],[logseq____"^15logseq____",[57,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[57,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",34,536870918]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",38,536870918]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u65259c90-62e2-4314-aacc-2dc91851ab69logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&=\\\\lg y logseq____& ,r\\\\\\\\\\nxlogseq____&=\\\\log_y10logseq____&,f\\\\\\\\\\nxlogseq____&=\\\\log_{10}ylogseq____&,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 2 logseq____&, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, r \\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",52,536870918]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",52,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u65259c90-7e52-4d69-bd48-d017e54aadcclogseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",66,536870918]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",63,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[59,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u65259c90-a551-4db3-b258-06a39ff168e8logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a\\\\sqrt{a}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^2-\\\\sqrt{a}logseq____&,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=\\\\sqrt{a^3}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^{\\\\frac32}logseq____&,r\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",46,536870918]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",46,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u65259c90-2e40-4474-b2cd-40c0c17a38c1logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\na^nlogseq____&=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____& a,blogseq____>0\\\\\\\\\\na^2b^2logseq____&=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&=a^{nm}\\\\\\\\\\na^0logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",42,536870918]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",42,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u65259c90-f355-4d19-b8a7-73d9adcd9fa8logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",76,536870918]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",67,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[62,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[62,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[62,logseq____"^Hlogseq____",25,536870918]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u65259c90-6f3e-416f-8e7d-6c65d259252elogseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",68,536870918]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",81,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[63,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[63,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[63,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u65259c90-2584-40ef-a5b6-2c56358bf71dlogseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",63,536870918]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",81,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[64,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[64,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[64,logseq____"^Hlogseq____",26,536870918]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u65259c90-c9f7-4860-a7b9-1bff38bae750logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&, a,b,logseq____>0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",51,536870918]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",57,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",34,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",38,536870918]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u65259c90-26d7-489b-88e7-ab4eafd85dd3logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\sqrt{x^4+6x^2y+9y^2}logseq____&=\\\\sqrt{(x^2+3y)^2}=x^2+3y\\\\\\\\\\n\\\\sqrt {x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&=\\\\sqrt{\\\\left(x + \\\\sqrt{x^2-y^2}\\\\right)\\\\left(x-\\\\sqrt{x^2-y^2}\\\\right)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{x^2-(x^2-y^2)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{y^2}=\\\\left|y\\\\right|\\\\\\\\\\n\\\\sqrt[5]{a\\\\sqrt[3]a}=\\\\sqrt[5]{\\\\sqrt[3]{a^3}\\\\sqrt[3]a}\\nlogseq____&=\\\\sqrt[5]{\\\\sqrt[3]{a^4}}\\n=\\\\sqrt[5]{a^\\\\frac43}\\n=a^{\\\\frac43\\\\frac15}=a^\\\\frac4{15}\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",49,536870918]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",63,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u65259c90-bba7-4410-b39d-9142a52bbde5logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",41,536870918]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[67,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[67,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[67,logseq____"^Hlogseq____",30,536870918]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u65259c90-cfed-4eea-8cd6-5d3de61e2fcblogseq____",536870918]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870918]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",42,536870918]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",81,536870918]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u65259c90-c586-486b-855f-b7d41f812621logseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Qlogseq____",logseq____"$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0logseq____&|logseq____&-q\\\\\\\\\\nx^2+pxlogseq____&=-qlogseq____&|logseq____&+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&|logseq____&\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&,logseq____&\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&|logseq____&-\\\\frac p2\\\\\\\\\\nxlogseq____&=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",56,536870918]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",56,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",37,536870918]],[logseq____"^15logseq____",[69,logseq____"^Hlogseq____",23,536870918]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u65259c90-9524-4f71-b6a6-88cebe3ec167logseq____",536870918]],[logseq____"^15logseq____",[70,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&=a^2+2ab+b^2logseq____&,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&=a^2-2ab+b^2logseq____&,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&=a^2-b^2logseq____&,\\\\text{ 3. Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",67,536870918]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",67,536870918]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[70,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u65259c90-07bf-427d-9c79-9a53437ee078logseq____",536870918]],[logseq____"^15logseq____",[71,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c} (a+b)^0logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 \\\\\\\\\\n(a+b)^1logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^2logseq____&logseq____&logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 2 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^3logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 3 logseq____&logseq____& 3 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^4logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 4 logseq____&logseq____& 6 logseq____&logseq____& 4 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^5logseq____&logseq____&logseq____& 1 logseq____&logseq____& 5 logseq____&logseq____& 10 logseq____&logseq____& 10 logseq____&logseq____& 5 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^6logseq____&logseq____& 1 logseq____&logseq____& 6 logseq____&logseq____& 15 logseq____&logseq____& 20 logseq____&logseq____& 15 logseq____&logseq____& 6 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^7logseq____&1 logseq____&logseq____& 7 logseq____&logseq____&21 logseq____&logseq____& 35 logseq____&logseq____& 35 logseq____&logseq____& \\\\cdots\\\\end{array}logseq____",536870918]],[logseq____"^15logseq____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",62,536870918]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",62,536870918]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[71,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u65259c90-7f80-4fac-b61b-b8faab826203logseq____",536870918]],[logseq____"^15logseq____",[72,logseq____"^Qlogseq____",logseq____"$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",48,536870918]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",48,536870918]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u65259c90-b965-4a63-9487-c12093ab7250logseq____",536870918]],[logseq____"^15logseq____",[73,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&= e^x + e^y logseq____& ,f \\\\\\\\\\ne^{x+y} logseq____&= e^x * x^y logseq____& ,r \\\\\\\\\\ne^{x+y}logseq____&=e^{xy} logseq____& ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=x+y logseq____& ,x+ylogseq____>c \\\\\\\\\\ne^{ln(x+y)}logseq____&=e^x*e^ylogseq____&,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=ln(e^x+y)logseq____&,x+ylogseq____>0\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",82,536870918]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",82,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",29,536870918]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[73,logseq____"^Hlogseq____",29,536870918]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u65259c90-4076-49e5-9019-bda88fb5f80elogseq____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____>0 constraintlogseq____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",63,536870918]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",63,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",36,536870918]],[logseq____"^15logseq____",[74,logseq____"^Hlogseq____",36,536870918]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u65259c90-8f56-469b-bba2-73fdee5d110elogseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nax^2+bx+clogseq____&=0logseq____&|:a\\\\quadlogseq____&a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&= 0\\\\\\\\\\nplogseq____&=\\\\frac ba,logseq____&q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&=0\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",64,536870918]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",81,536870918]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[75,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u65259c90-bb0f-47cc-9a31-8d4972c9821blogseq____",536870918]],[logseq____"^15logseq____",[76,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&=\\\\frac{2a}{2b}\\nlogseq____&=\\\\frac ab\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",70,536870918]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",67,536870918]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u65259c90-edce-4f1f-83ef-4bd8800b9942logseq____",536870918]],[logseq____"^15logseq____",[77,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____",536870918]],[logseq____"^15logseq____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",40,536870918]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",55,536870918]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u65259c90-93e7-4c69-bdb4-40188d953803logseq____",536870918]],[logseq____"^15logseq____",[78,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&=\\\\begin{cases}\\ny logseq____&\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&\\\\text{ falls } ylogseq____<0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[78,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[78,logseq____"^Flogseq____",59,536870918]],[logseq____"^15logseq____",[78,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[78,logseq____"^Vlogseq____",63,536870918]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u65259c90-c8b4-4351-bb95-3038a1129c39logseq____",536870918]],[logseq____"^15logseq____",[79,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870918]],[logseq____"^15logseq____",[79,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[79,logseq____"^Flogseq____",48,536870918]],[logseq____"^15logseq____",[79,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[79,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[79,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[79,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[79,logseq____"^Hlogseq____",31,536870918]],[logseq____"^15logseq____",[79,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u65259c90-022d-489a-a8a6-9a791c41af4blogseq____",536870918]],[logseq____"^15logseq____",[80,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",54,536870918]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",79,536870918]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[80,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u65259c90-457c-4678-8acd-a175d4f289b3logseq____",536870918]],[logseq____"^15logseq____",[81,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[81,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[81,logseq____"^Flogseq____",67,536870918]],[logseq____"^15logseq____",[81,logseq____"^Xlogseq____",35,536870918]],[logseq____"^15logseq____",[81,logseq____"^Vlogseq____",35,536870918]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",35,536870918]],[logseq____"^15logseq____",[81,logseq____"^?logseq____",[logseq____"^ 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