MK-MO 2010 Problem 2

Let $a,b,c$ be positive real numbers for which $a+b+c=3$ . Prove the inequality $\frac{a^3+2}{b+2}+\frac{b^3+2}{c+2}+\frac{c^3+2}{a+2}\ge3$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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