olymmath

SE-SKOLORNAS 2015 Problem 4

    Solve the system of equations {xlog⁡x+ylog⁡y+zlog⁡x=0log⁡xx+log⁡yy+log⁡zz=0\left\{\begin{array}{l} x \log x+y \log y+z \log x=0 \dfrac{\log x}{x}+\dfrac{\log y}{y}+\dfrac{\log z}{z}=0 \end{array} \right.

    Dataset text AI-MO AoPS. Quoted with source.

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