doturitip9

2022-07-07

Find $\frac{{x}^{2}}{{y}^{2}}$ + $\frac{{y}^{2}}{{x}^{2}}$

If $\frac{x}{y}$ + $\frac{y}{x}$ = 3

If $\frac{x}{y}$ + $\frac{y}{x}$ = 3

poquetahr

Beginner2022-07-08Added 18 answers

$\begin{array}{rl}\frac{x}{y}+\frac{y}{x}=3& \u27f9{(\frac{x}{y}+\frac{y}{x})}^{2}=9\\ & \u27f9\frac{{x}^{2}}{{y}^{2}}+\frac{{y}^{2}}{{x}^{2}}=9-2=7\end{array}$

Gretchen Schwartz

Beginner2022-07-09Added 5 answers

Hint: Look at:

${(\frac{x}{y}+\frac{y}{x})}^{2}={3}^{2}=9$

Why to look at this? We know if we expand we will have a $(\frac{x}{y}{)}^{2}=\frac{{x}^{2}}{{y}^{2}}$ term and a $(\frac{y}{x}{)}^{2}=\frac{{y}^{2}}{{x}^{2}}$ term so this might be worth a try.\

${(\frac{x}{y}+\frac{y}{x})}^{2}={3}^{2}=9$

Why to look at this? We know if we expand we will have a $(\frac{x}{y}{)}^{2}=\frac{{x}^{2}}{{y}^{2}}$ term and a $(\frac{y}{x}{)}^{2}=\frac{{y}^{2}}{{x}^{2}}$ term so this might be worth a try.\

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