Olympiad for grade 10

Algebra Level 4

Let \[a,b,c> 0,abc=1\] Let the minimum of P is M \[P= \frac{a^2}{\sqrt{2+2ab}}+\frac{b^2}{\sqrt{2+2bc}}+\frac{c^2}{\sqrt{2+2ca}}\] If \[M=\frac{m}{n}\] Find the value of m+n if \( \gcd{m,n}=1\)

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