Question

упростите выражение(x/y+y/x+2)*1/(x+y)^2,при x=√2; y=√8

Answer 1

$( frac{x}{y} + frac{y}{x} +2)* frac{1}{(x+y)^2}= frac{x^2+2xy+y^2}{xy(x^2+2xy+y^2)}= frac{1}{xy}= frac{1}{ sqrt{2} sqrt{8} }= frac{1}{ sqrt{16} }=1/4$