Easy Inequality

Algebra Level 3

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

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