nie tylko wynik 3 zadanie 3/224wykonaj dzialaniaa) (√5+1)²b) (2√3+4)²
c) ( √3+ √2/2)²
d) (3√2 + 2√6)²
Wzór skróconego mnożenia
a)
b)
c)
d)
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Wzór skróconego mnożenia![(a+b)^2=a^2+2*a*b+b^2 (a+b)^2=a^2+2*a*b+b^2](https://tex.z-dn.net/?f=%28a%2Bb%29%5E2%3Da%5E2%2B2%2Aa%2Ab%2Bb%5E2)
a)![(\sqrt5+1)^2=(\sqrt5)^2+2*1*\sqrt5+(1)^2=6+2\sqrt5 (\sqrt5+1)^2=(\sqrt5)^2+2*1*\sqrt5+(1)^2=6+2\sqrt5](https://tex.z-dn.net/?f=%28%5Csqrt5%2B1%29%5E2%3D%28%5Csqrt5%29%5E2%2B2%2A1%2A%5Csqrt5%2B%281%29%5E2%3D6%2B2%5Csqrt5)
b)![(2\sqrt3+4)^2=(2\sqrt3)^2+2*4*2\sqrt3+(4)^2=28+16\sqrt3 (2\sqrt3+4)^2=(2\sqrt3)^2+2*4*2\sqrt3+(4)^2=28+16\sqrt3](https://tex.z-dn.net/?f=%282%5Csqrt3%2B4%29%5E2%3D%282%5Csqrt3%29%5E2%2B2%2A4%2A2%5Csqrt3%2B%284%29%5E2%3D28%2B16%5Csqrt3)
c)![(\sqrt3+\frac{\sqrt2}{2})^2=(\sqrt3)^2+2*\sqrt3*\frac{\sqrt2}{2}+(\frac{\sqrt2}{2})^2=3\frac{1}{2}+\sqrt6 (\sqrt3+\frac{\sqrt2}{2})^2=(\sqrt3)^2+2*\sqrt3*\frac{\sqrt2}{2}+(\frac{\sqrt2}{2})^2=3\frac{1}{2}+\sqrt6](https://tex.z-dn.net/?f=%28%5Csqrt3%2B%5Cfrac%7B%5Csqrt2%7D%7B2%7D%29%5E2%3D%28%5Csqrt3%29%5E2%2B2%2A%5Csqrt3%2A%5Cfrac%7B%5Csqrt2%7D%7B2%7D%2B%28%5Cfrac%7B%5Csqrt2%7D%7B2%7D%29%5E2%3D3%5Cfrac%7B1%7D%7B2%7D%2B%5Csqrt6)
d)![(3\sqrt2+2\sqrt6)^2=(3\sqrt2)^2+2*3\sqrt2*2\sqrt6+(2\sqrt6)^2=18+12\sqrt{12}+24=42+12\sqrt{12} (3\sqrt2+2\sqrt6)^2=(3\sqrt2)^2+2*3\sqrt2*2\sqrt6+(2\sqrt6)^2=18+12\sqrt{12}+24=42+12\sqrt{12}](https://tex.z-dn.net/?f=%283%5Csqrt2%2B2%5Csqrt6%29%5E2%3D%283%5Csqrt2%29%5E2%2B2%2A3%5Csqrt2%2A2%5Csqrt6%2B%282%5Csqrt6%29%5E2%3D18%2B12%5Csqrt%7B12%7D%2B24%3D42%2B12%5Csqrt%7B12%7D)