9- Inequalities

Let $a, b, c\geq1$ be positive real numbers such that

$a + b + c = 6$.

Prove that

$(a^2 + 2)(b^2 + 2)(c^2 + 2) ≤ 216$. 

Proposed by Mihai Piticari, Campulung Moldovenesc, Romania

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