Question

Найти значение выражения. При х=4-2√5 у=8-√5

Answer 1

$\frac{x^2}{x^2+2xy}:\frac{x}{x^2-4y^2}=\frac{x^2\cdot (x-2y)(x+2y)}{x(x+2y)\cdot x^2}= \frac{x-2y}{x}=\\\\=1-\frac{2y}{x}=1-\frac{2(8-\sqrt5)}{4-2\sqrt5}=1-\frac{8-\sqrt5}{2-\sqrt5}=\\\\=1-\frac{(8-\sqrt5)(2-\sqrt5)}{4-5}=1-\frac{21-10\sqrt5}{-1}=1-21+10\sqrt5=\\\\=10\sqrt5-20=10(\sqrt5-2)$