# Curious Condition

Algebra Level 5

Positive reals $$x,y,z\ge \dfrac{\sqrt{3}}{3}$$ satisfy the condition $$xyz+x+y-z=0$$. If $$kxyz-xy-yz-zx\ge 1$$ is always true, the the minimum value of $$k$$ can be expressed as $$\dfrac{a\sqrt{b}}{c}$$ for positive integers $$a,b,c$$ with $$a,c$$ coprime and $$b$$ square-free.

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

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