Just do it bro

Algebra Level 5

\[[(a+b)^2+(b+c)^2+(c+a)^2] \left[\frac{1}{(a-b)^2}+\frac{1}{(b-c)^2}+\frac{1}{(c-a)^2}\right]\]

Given that \(a,b\) and \(c\) are distinct non-negative real numbers, and let the minimum value of the expression above be denoted as \(Q\), find \( \lfloor 1000Q \rfloor \).


Inspiration.

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