Olympiad for grade 10

Algebra Level 4

Let a,b,c>0,abc=1a,b,c> 0,abc=1 Let the minimum of P is M P=a22+2ab+b22+2bc+c22+2caP= \frac{a^2}{\sqrt{2+2ab}}+\frac{b^2}{\sqrt{2+2bc}}+\frac{c^2}{\sqrt{2+2ca}} If M=mnM=\frac{m}{n} Find the value of m+n if gcdm,n=1 \gcd{m,n}=1

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