Easy Inequality

Algebra Level 3

If a+b=1 a + b = 1 . Then the minimum value of (a+1a)2+(b+1b)2(a + \frac{1}{a} )^2 + (b + \frac{1}{b} )^2 is of the form "m/nm/n" . Where mm and nn are coprime. Then the value of m+nm+n ?

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