4 - Inequalities

Let x, y, z be positive real numbers such that 

$x ≤ 1, y ≤ 2$ and $x + y + z = 6$. 

Prove that 

$(x + 1)(y + 1)(z + 1) ≥ 4xyz$. 

Proposed by Marius Stanean, Zalau, Romania

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