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US-TST 2009 Problem 7

    Find all triples (x,y,z)(x,y,z) of real numbers that satisfy the system of equations {x3=3x−12y+50,y3=12y+3z−2,z3=27z+27x.\begin{cases}x^3 = 3x-12y+50, y^3 = 12y+3z-2, z^3 = 27z + 27x. \end{cases}

    Razvan Gelca.

    Dataset text AI-MO AoPS. Quoted with source.

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