# Real function

Algebra Level 5

You are given that $$a,b$$ and $$c$$ are positive real numbers satisfying $$a+b+c\leq \frac{3}{2}$$. Let $$P$$ is the minimum value of the expression below.

$\sum_{\text{cyclic}} \sqrt{2a^2+\frac{1}{a^2b^2}+\frac{2}{b}}$ Find $$\left \lfloor 1000P \right \rfloor$$

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