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If x ,\ y , z are not all zero and if a ...

If `x ,\ y , z` are not all zero and if `a x+b y+c z=0; b x+c y+a z=0; c x+a y+b z=0` Prove that `x : y : z=1:1:1\ or\ 1:omega:omega^2or\ 1:omega^2:omegadot`

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