Quadratic Dilemma

Algebra Level 3

\[ \frac{x^2}{10}+\frac{28}{x}=\frac{7x}{5}-\frac{40}{x^2}\]

The equation above has 4 real roots \(x_1\), \(x_2\), \(x_3\), and \(x_4\) such that \(x_1<x_2<x_3<x_4\). Find the value of \(x_1x_3+x_2x_4\).

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