Oblicz wartosc wyrazenia: 2(x-y) (x+y) - 3(x+2y) do potegi 2 + (x-y) do potegi 2 gdy x i y=pierwiast.... Question from @krysia9423

November 2018 2 12 Report

Oblicz wartosc wyrazenia: 2(x-y) (x+y) - 3(x+2y) do potegi 2 + (x-y) do potegi 2 gdy x $\sqrt{2}$ i y=pierwiastek z 2 dzielone przez 2
Z gory dziekuje za pomoc :)

animaldk $2(x-y)(x+y)-3(x+2y)^2+(x-y)^2\\=2(x^2-y^2)-3(x^2+4xy+4y^2)+x^2-2xy+y^2\\=2x^2-2y^2-3x^2-12xy-12y^2+x^2-2xy+y^2\\=-12y^2-14xy\\\\x=\sqrt2;\ y=\frac{\sqrt2}{2}\\\\-12\cdot(\frac{\sqrt2}{2})^2-14\cdot\sqrt2\cdot\frac{\sqrt2}{2}=-12\cdot\frac{2}{4}-14\\\\=-3\cdot2-14=-6-14=-20$

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heh Wzory skróconego mnożenia:
(a+b)²=a²+2ab+b² - kwadrat sumy;
(a-b)²=a²-2ab+b² - kwadrat różnicy;
a²-b²=(a-b)(a+b) - różnica kwadratów.
=============================================
$2(x-y)(x+y)-3(x+2y)^{2}+(x-y)^{2}=\\
=2(x^{2}-y^{2})-3(x^{2}+4xy+4y^{2})+x^{2}-2xy+y^{2}=\\
=2x^{2}-y^{2}-3x^{2}-12xy-12y^{2}+x^{2}-2xy+y^{2}=\\
=-14xy-12y^{2}=\\
---\\
x=\sqrt{2}\\
y=\frac{\sqrt{2}}{2}\\
---\\
=-14*\sqrt{2}*\frac{\sqrt{2}}{2}-12*(\frac{\sqrt{2}}{2})^{2}=\\
=-7*\sqrt{2}^{2}-12*\frac{2}{4}=\\
=-7*2-3*2=-14-6=-20$

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