BALKAN 2005 Problem 3

Let $a,b,c$ be positive real numbers. Prove the inequality $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\geq a+b+c+\frac{4(a-b)^2}{a+b+c}.$

When does equality occur?

Dataset text AoPS wiki problems. Quoted with source.

Solutions

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