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If x=a+b,y=a gamma+b beta and z=abeta+ ...

If `x=a+b,y=a gamma+b beta and z=abeta+ b gamma` , where `gamma and beta` are the imaginary cube roots ofunity, then `xyz=`

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Since `alpha Beta` are the complex cube roots of unity
`therefore` We take `alpha = omega= omega^2`
Now `xyz=(a+b)(a alpha +b beta)(alpha beta + b beta)`
`= (a+b)[a^2alpha beta +a b (alpha^2 +beta ^2)+b^2 alpha beta]`
`=(a+b)(a^2-ab +b^2) [ therefore 1+ omega+omega^2 =0 and omega^3 =1]`
`=a^3 +b^3`
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