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Question Number 201302 by hardmath last updated on 03/Dec/23

$$\{\begin{array}{l}{\mathrm{x}}^2+{\mathrm{y}}^{-2}=4\\ {\mathrm{x}}^{-2}+{\mathrm{y}}^2=5\end{array}\mathrm{find}:\frac{\mathrm{y}}{\mathrm{x}}=?$$

Answered by witcher3 last updated on 03/Dec/23

$$\left(1\right)\ast \left(2\right)\iff 2+{\left(\mathrm{xy}\right)}^2+\frac{1}{{\left(\mathrm{xy}\right)}^2}=20$$$$\left(2\right)/\left(1\right)\Rightarrow \frac{1+{\mathrm{x}}^2{\mathrm{y}}^2}{{\mathrm{x}}^2}.\frac{{\mathrm{y}}^2}{{\mathrm{x}}^2{\mathrm{y}}^2+1}=\frac{5}{4}$$$$\frac{\mathrm{y}}{\mathrm{x}}=\underset{-}{+}\sqrt{\frac{5}{4}}$$

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