KZ-MO 2019 Problem 1

Prove for any positives $a,b,c$ the inequality $\sqrt[3]{\dfrac{a}{b}}+\sqrt[5]{\dfrac{b}{c}}+\sqrt[7]{\dfrac{c}{a}}>\dfrac{5}{2}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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