ELMO SL 2019 A1

Let $a$ , $b$ , $c$ be positive reals such that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1$ . Show that $a^abc+b^bca+c^cab\ge 27bc+27ca+27ab.$

Proposed by Milan Haiman

Dataset text AoPS wiki problems. Quoted with source.

Solutions

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