# Find x 2 </msup> y 2 </msup> </mfrac> +

Find $\frac{{x}^{2}}{{y}^{2}}$ + $\frac{{y}^{2}}{{x}^{2}}$
If $\frac{x}{y}$ + $\frac{y}{x}$ = 3
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poquetahr
$\begin{array}{rl}\frac{x}{y}+\frac{y}{x}=3& ⟹{\left(\frac{x}{y}+\frac{y}{x}\right)}^{2}=9\\ & ⟹\frac{{x}^{2}}{{y}^{2}}+\frac{{y}^{2}}{{x}^{2}}=9-2=7\end{array}$

Gretchen Schwartz
Hint: Look at:
${\left(\frac{x}{y}+\frac{y}{x}\right)}^{2}={3}^{2}=9$
Why to look at this? We know if we expand we will have a $\left(\frac{x}{y}{\right)}^{2}=\frac{{x}^{2}}{{y}^{2}}$ term and a $\left(\frac{y}{x}{\right)}^{2}=\frac{{y}^{2}}{{x}^{2}}$ term so this might be worth a try.\