VMO 2008 Problem 6

Let $x, y, z$ be distinct non-negative real numbers. Prove that

$\frac{1}{(x-y)^2} + \frac{1}{(y-z)^2} + \frac{1}{(z-x)^2} \geq \frac{4}{xy + yz + zx}.$

When does the equality hold?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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