# Such Big Denominator you got there!

Algebra Level 3

We have $$3$$ non-negative real numbers $${a,b,c}$$ such that $$abc=1$$.

When the maximum value of the expression

$\dfrac{2}{2ab+2ac+2bc+a^2+b^2+c^2}$

is expressed in the form $$\dfrac{x}{y}$$ for coprime positive integers $$x$$ and $$y$$

What is the value of $$x+y$$?

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