olymmath

PL-OM 1997 Problem 2

    Znaleźć wszystkie trójki liczb rzeczywistych x,y,zx, y, z spełniające układ równań {3(x2+y2+z2)=1x2y2+y2z2+z2x2=xyz(x+y+z)3.\begin{cases} 3(x^2 + y^2 + z^2) = 1 \\ x^2y^2 + y^2z^2 + z^2x^2 = xyz(x + y + z)^3. \end{cases}

    Official text Polish Mathematical Olympiad 1997 official paper, page 1. Quoted with source.

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