$\left\{\begin{matrix} \sqrt{{{x}^{2}}+\frac{1}{{{x}^{2}}}}+\sqrt{{{y}^{2}}+\frac{1}{{{y}^{2}}}}=2\sqrt{5} \\ \left( x+y \right)\left( \frac{1}{xy}+1 \right)=3\sqrt{2} \end{matrix}\right.$
$\left\{\begin{matrix} \sqrt{{{x}^{2}}+\frac{1}{{{x}^{2}}}}+\sqrt{{{y}^{2}}+\frac{1}{{{y}^{2}}}}=2\sqrt{5} \\ \left( x+y \right)\left( \frac{1}{xy}+1 \right)=3\sqrt{2} \end{matrix}\right.$
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