Wildest Equation

Algebra Level 4

Suppose that \(x, y\) and \(z\) are real numbers and \(y \geq 1\). Find \(\sqrt{x^2 + y^2 +z^2}\) such that

\[\large{x+y = 1-2\sqrt{xy-x} - \sqrt{1-2y+y^2 +z^4}}.\]

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