# 2012 USAJMO Problems/Problem 3

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## Problem

Let $a$, $b$, $c$ be positive real numbers. Prove that $$\frac{a^3 + 3b^3}{5a + b} + \frac{b^3 + 3c^3}{5b + c} + \frac{c^3 + 3a^3}{5c + a} \ge \frac{2}{3} (a^2 + b^2 + c^2).$$