# 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 $$\lfloor m \rfloor$$.

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