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ZA-SAMO 2001 Problem 2

    Find all triples (x,y,z)(x,y,z) of real numbers that satisfy x(1−y2)(1−z2)+y(1−z2)(1−x2)+z(1−x2)(1−y2)=4xyz=4(x+y+z).\begin{aligned} & x\left(1 - y^2\right)\left(1 - z^2\right) + y\left(1 - z^2\right)\left(1 - x^2\right) + z\left(1 - x^2\right)\left(1 - y^2\right) & = 4xyz & = 4(x + y + z). \end{aligned}

    Dataset text AI-MO AoPS. Quoted with source.

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