IR-MO-R2 2016 Problem 1

If $0<a\leq b\leq c$ prove that $\frac{(c-a)^2}{6c}\leq \frac{a+b+c}{3}-\frac{3}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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