Question

(√х-√у)в квадрате+(√х+√у)в квадрате=?

Answer 1

$(\sqrt{x}-\sqrt{y})^{2}+(\sqrt{x}+\sqrt{y})^{2}=((\sqrt{x})^{2}-2\sqrt{x}\cdot\sqrt{y}+(-\sqrt{y})^{2})+ ((\sqrt{x})^{2}+2\sqrt{x}\cdot\sqrt{y}+(\sqrt{y})^{2})=(x-2\sqrt{xy}+y)+ (x+2\sqrt{xy}+y)=x-2\sqrt{xy}+y+x+2\sqrt{xy}+y=(x+x)+(2\sqrt{xy}-2\sqrt{xy})+(y+y)=2x+2y$

Answer 2

(√х-√у)²+(√х+√у)²=(√х)²-2√х√у+(√У)²+(√х)²+2√х√у+(√У)²=х-2√х√у+у+х+2√х√у+у=2х+2у