# Maximize the System

Algebra Level pending

Consider the system $$x + y = z + u, 2xy = zu$$. Find the greatest value of the real constant $$m$$ such that $$m ≤ \frac{x}{y}$$ for every positive integer solution $$x, y, z, u$$ of the system where $$x ≥ y$$.

Express your answer up to three digit places. This problem is not original.

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