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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