Question

очень срочно решите пожалуйста , даю 100 балов , 10 класс

Answer 1

  $\displaystyle \tt \left(\frac{x^{\tfrac{1}{2}}+y^{\tfrac{1}{2}}}{(x+y)^{\tfrac{1}{2}}}-\frac{(x+y)^{\tfrac{1}{2}}}{x^{\tfrac{1}{2}}+y^{\tfrac{1}{2}}}\right)^{-2}-\frac{x+y}{2\sqrt{xy}}=\left(\frac{(\sqrt{x}+\sqrt{y})^{2}-(\sqrt{x+y})^{2}}{\sqrt{x+y}\cdot (\sqrt{x}+\sqrt{y})\right)^{-2}-\frac{x+y}{2\sqrt{xy}}}=\\\\=\left(\frac{x+y+2\sqrt{xy}-x-y}{\sqrt{x+y}\cdot(\sqrt{x}+\sqrt{y})}\right)^{-2}-\frac{x+y}{2\sqrt{xy}}=\frac{(x+y)(x+y+2\sqrt{xy})}{(2\sqrt{xy})^{2}}-\frac{x+y}{2\sqrt{xy}}=$

$\displaystyle \tt {}\\\\=\frac{(x+y)(x+y+2\sqrt{xy})-(x+y)\cdot 2\sqrt{xy}}{4xy}=\frac{(x+y)(x+y+2\sqrt{xy}-2\sqrt{xy})}{4xy}=\\\\=\frac{(x+y)^{2}}{4xy};$