olymmath

VMO 2006 Problem 1

    Solve the following system of equations in real numbers: {x2−2x+6⋅log⁡3(6−y)=xy2−2y+6⋅log⁡3(6−z)=yz2−2z+6⋅log⁡3(6−x)=z.\begin{cases} \sqrt{x^2-2x+6}\cdot \log_{3}(6-y) =x \sqrt{y^2-2y+6}\cdot \log_{3}(6-z)=y \sqrt{z^2-2z+6}\cdot\log_{3}(6-x)=z \end{cases}.

    Dataset text AI-MO AoPS. Quoted with source.

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