I have three manifolds $z = 1/2*(x-\sqrt{x^2+4xy-4y^2})$, $y = 1/2*(z-\sqrt{z^2+4zx-4x^2})$, and $x = 1/2*(y-\sqrt{y^2+4yz-4z^2})$. My thinking is that they don't intersect, but I can't prove it. I know they intersect at zero but I want to know if they intersect anywhere else?
Intesection of manifolds
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optimization