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Hard Inequality

Source: 2009 József Wildt International Mathematical Competition

April 15, 2020
inequalities

Problem Statement

Let aa, bb, cc be positive real numbers such that a+b+c=1a + b + c = 1. Prove that (1+ab+c)1−abc(1+bc+a)1−bca(1+ca+b)1−cab3≥64\sqrt[3]{\left (\frac{1+a}{b+c}\right )^{\frac{1-a}{bc}}\left (\frac{1+b}{c+a}\right )^{\frac{1-b}{ca}}\left (\frac{1+c}{a+b}\right )^{\frac{1-c}{ab}}} \geq 64
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