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If alpha, beta, gamma are the cube roots...

If `alpha, beta, gamma` are the cube roots of a negative number p, then for any three real numbers x,y,z the value of `(x alpha+y beta+ z gamma)/(x beta +y gamma+z alpha)` is

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The correct Answer is:
`omega^(2)`
`(xalpha+ybeta+zgamma)/(zbeta+ygamma+zalpha)=(x(p)^(1//3)+y(p)^(1//3)+omega+z(p)^(1//3)omega^2omega^2x(+yomega+zomega^2))/(x(p)^(1//3)omega^2+y(p)^(1//3)omega^(3)+z(p)^(1//3)omegaomega^2(xomega+yomega^2+z))`
`(omega^2(x+yomega+zomega^2))/(x+yomega +zomega^2)=omega`
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