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OBM 2023 Problem 4

    Sejam x,y,zx, y, z três números reais distintos tais que

    {x2−x=yzy2−y=zxz2−z=xy.\begin{cases} x^2 - x = yz \\ y^2 - y = zx \\ z^2 - z = xy \end{cases}.

    Prove que −13<x,y,z<1-\frac{1}{3} < x, y, z < 1.

    Official text Brazilian Mathematical Olympiad 2023 official paper, page 2. Quoted with source.

    A model read this text from the scan of the paper by OCR, with vision/claude@2.1.318 (claude-opus-5-5). No person has checked it against the paper yet.

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