# Definitely not $$x=y=z$$

Algebra Level 5

Let $$x, y, z$$ be distinct positive reals satisfying $$xy+yz=2{ z }^{ 2 }$$ and $$2x\le z$$. Find the maximum value of

$\large \frac { x }{ x-y } +\frac { y }{ y-z } +\frac { z }{ z-x }$

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