# Careful with AM-GM!

Algebra Level 5

Let $$x_1, x_2, x_3, x_4$$ be distinct real numbers such that $$x_1 x_3 = x_2 x_4$$ and $\frac{x_1}{x_2}+\frac{x_2}{x_3}+\frac{x_3}{x_4}+\frac{x_4}{x_1}=4$

Find the maximum value of $\frac{x_1}{x_3}+\frac{x_2}{x_4}+\frac{x_3}{x_1}+\frac{x_4}{x_2}$.

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