# Greece National Olympiad Problem 4

Algebra Level 5

Let $a,b,c$ be positive real numbers with sum $6$. Find the maximum value of $S = \sqrt[3]{{{a^2} + 2bc}} + \sqrt[3]{{{b^2} + 2ca}} + \sqrt[3]{{{c^2} + 2ab}}.$

This problem is part of this set.

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