اگر ${{x}^{۲}}+{{y}^{۲}}+۶xy=۰$ باشد حاصل عبارت ${{\left( \frac{x+y}{x-y} \right)}^{۲}}$ برابر کدام است؟
$\begin{align} & {{\left( \frac{x+y}{x-y} \right)}^{2}}=\frac{{{x}^{2}}+{{y}^{2}}+2xy}{{{x}^{2}}+{{y}^{2}}-2xy}= \\ & {{x}^{2}}+{{y}^{2}}=-6xy\to \frac{-6xy+2xy}{-6xy-2xy}=\frac{-4xy}{-8xy}=\frac{1}{2} \\ \end{align}$