olymmath

OIM 2016 Problem 2

    Find all positive real numbers (x,y,z)(x,y,z) such that: x=1y2+y−1x = \frac{1}{y^2+y-1} y=1z2+z−1y = \frac{1}{z^2+z-1} z=1x2+x−1z = \frac{1}{x^2+x-1}

    Dataset text AI-MO AoPS. Quoted with source.

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