Such Big Denominator you got there!

Algebra Level 3

We have 33 non-negative real numbers a,b,c{a,b,c} such that abc=1abc=1.

When the maximum value of the expression

22ab+2ac+2bc+a2+b2+c2\dfrac{2}{2ab+2ac+2bc+a^2+b^2+c^2}

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

What is the value of x+yx+y?

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