Wildest Equation

Algebra Level 4

Suppose that x,yx, y and zz are real numbers and y1y \geq 1. Find x2+y2+z2\sqrt{x^2 + y^2 +z^2} such that

x+y=12xyx12y+y2+z4.\large{x+y = 1-2\sqrt{xy-x} - \sqrt{1-2y+y^2 +z^4}}.

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