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a8+b−c3+b8+c−a3+c8+a−b3a\sqrt[3]{8+b-c}+b\sqrt[3]{8+c-a}+c\sqrt[3]{8+a-b}a38+b−c+b38+c−a+c38+a−b
Let a,ba,ba,b and ccc be non-negative numbers satisfying a2+b2+c2=13a^2+b^2+c^2=\dfrac{1}{3}a2+b2+c2=31.
Find the maximum value of the expression above.
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