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ILL 1985 Problem 4

    Let x,yx, y , and zz be real numbers satisfying x+y+z=xyz.x + y + z = xyz. Prove that x(1−y2)(1−z2)+y(1−z2)(1−x2)+z(1−x2)(1−y2)=4xyz.x(1 - y^2)(1 - z^2) + y(1 -z^2)(1 - x^2) + z(1 - x^2)(1 - y^2) = 4xyz.

    Dataset text AI-MO AoPS. Quoted with source.

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