7 - Inequalities

Let $a, b, c$ be positive real numbers. 

Prove that

$\dfrac{1}{a + 2b + 5c} + \dfrac{1}{ b + 2c + 5a} + $

$+\dfrac{1}{ c + 2a + 5b} ≤ \dfrac{9}{8}\dfrac{a + b + c}{ (\sqrt{ab} + \sqrt{bc} + \sqrt{ac})^ 2}$.

Proposed by Tran Bach Hai, Bucharest, Romania

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