# 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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