Minimum value#3

Algebra Level 4

Non-negative real numbers \(a,b,c\) are such that \(a+b+c=2017\). Find the minimum value of

\[ C=\sqrt [ 3 ]{ 4\left( { a }^{ 3 }+{ b }^{ 3 } \right) } +\sqrt [ 3 ]{ 4\left( { b }^{ 3 }+{ c }^{ 3 } \right) } +\sqrt [ 3 ]{ 4\left( { c }^{ 3 }+{ a }^{ 3 } \right) } . \]

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