Question

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

Answer 1

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