1 - Inequalities

Let $a, b, c$ be positive real numbers such that 

$a^2 + b^2 + c^2 + abc = 4$.

Prove that

$a + b + c ≤ \sqrt{2 − a} + \sqrt{2 − b} + \sqrt{2 − c}$.

Proposed by An Zhen-ping, Xianyang Normal University, China

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