# Just do it

Algebra Level 5

$\frac{b+c}{b^2+c^2+2(ab+bc+ac)}+\frac{a+c}{a^2+c^2+2(ab+bc+ac)}+\frac{a+b}{a^2+b^2+2(ab+bc+ac)}$

Given that $$a,b$$ and $$c$$ are positive reals satisfying $$a^2b^2+b^2c^2+a^2c^2\leq666a^2b^2c^2$$. Let $$P$$ denote the maximum value of the expression above.

Find $$10P$$, round to the nearest integer.

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