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NL-NWO 2018 Problem 3

    Determine all triples (x,y,z)(x, y,z) consisting of three distinct real numbers, that satisfy the following system of equations: {x2+y2=−x+3y+zy2+z2=x+3y−zx2+z2=2x+2y−z\begin {cases}x^2 + y^2 = -x + 3y + z y^2 + z^2 = x + 3y - z x^2 + z^2 = 2x + 2y - z \end {cases}

    Dataset text AI-MO AoPS. Quoted with source.

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