# Try to handle this one instead

Algebra Level 4

$f(x,y,z) = 2x^2+2y^2-2z^2+\dfrac{7}{xy}+\dfrac{1}{z}$

There exists three pairwise distinct numbers $$a,b$$ and $$c$$ that satisfies

$f(a,b,c) = f(b,c,a) = f(c,a,b)$

Given that $$abc = \dfrac{m}{n}$$, where $$m$$ and $$n$$ are positive coprime integers, find the value of $$m+n$$

Inspiration

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