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Algebra Level 5

\[\large{\begin{cases} 2(x^3-3x)=y^3+3y \\ 2(x^2-1)=5y^2+1\end{cases}}\]

Let \( (x_1, y_1) , (x_2, y_2) ,\ldots , (x_n, y_n) \) be all real pairs of the solutions of \((x,y) \) satisfying the equation above. Compute \( \displaystyle \prod_{m=1}^n x_m y_m \).

Give your answer to 2 decimal places.

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