# Can You Handle This One

Algebra Level 4

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

There are three pairwise distinct numbers $$a,b,c$$ that satisfies the above equation in a way such that $$f(a,b,c)= f(b,c,a)=f(c,a,b)$$.

What is $$a+b+c$$?

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