Cool Inequality 7-90 Followers Problem!

Algebra Level 5

\[\large{|ab\left( { a }^{ 2 }-{ b }^{ 2 } \right) +bc\left( { b }^{ 2 }-{ c }^{ 2 } \right) +ca\left( { c }^{ 2 }-{ a }^{ 2 } \right) |\le M{ \left( { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 } \right) }^{ 2 }}\]

For all real numbers \(a,b,c\) the above inequality is satisfied. If the smallest value of constant \(M\) can be expressed as

\[\large{\frac { A }{ B } \sqrt { C } }\]

for some co-prime integers \(A\) and \(B\) and square-free number \(C\). Find \(A+B+C\)

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