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- #1

- Jan 26, 2012

- 4,198

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Find all pairs of real numbers $(x,y)$ satisfying the system of equations

\begin{align*}

\frac{1}{x} + \frac{1}{2y} &= (x^2+3y^2)(3x^2+y^2) \\

\frac{1}{x} - \frac{1}{2y} &= 2(y^4-x^4).

\end{align*}

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