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If $x, y, z$ are complex numbers, how can I solve this system of equations \begin{cases} x(x-y)(x-z)=3;\ \\y(y-z)(y-x)=3;\ \\z(z-x)(z-y)=3. \end{cases}

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    I guess you should divide first equation by the second one,the second one by the third one...etc2011-12-01
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    I have tried, however I can not get conclusion.2011-12-01
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    ,I don't see any other approach to this problem...2011-12-01
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    The answer consists of the roots of the equation $z^3=1$.2011-12-01

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