KMO 2009 Problem 2

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

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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