Wonderful property usage

Algebra Level 4

Give that \(a\) and \(b\) are positive numbers such that their sum equals to 1, and denote \(m\) as the minimum value of \( \left(a + \frac1a\right)^2 + \left(b+\frac1b\right)^2 \). Find the value of \(\lfloor m \rfloor \).


You can try my other sequences And series problems by clicking here : Part II and here : Part I .
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