Minimum value#3

Algebra Level 4

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

C=4(a3+b3)3+4(b3+c3)3+4(c3+a3)3. 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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