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NL-BXMO-TST 2021 Problem 2

    Find all triplets (x,y,z)(x, y, z) of real numbers for which {x2−yz=∣y−z∣+1y2−zx=∣z−x∣+1z2−xy=∣x−y∣+1\begin{cases}x^2- yz = |y-z| +1 y^2 - zx = |z-x| +1 z^2 -xy = |x-y| + 1 \end{cases}

    Dataset text AI-MO AoPS. Quoted with source.

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