Problem

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Tags: inequalities, algebra, Kosovo



Let $a,b$ and $c$ be positive real numbers such that $a^5+b^5+c^5=ab^2+bc^2+ca^2$. Prove the inequality: $$\frac{a^2+b^2}{b}+\frac{b^2+c^2}{c}+\frac{c^2+a^2}{a}\geq 2(ab+bc+ca).$$