If `alpha,beta,gamma` are the cube roots of p then for any `x,y` and `z` `(xalpha+ybeta+zgamma)/(xbeta+ygamma+zalpha)` is

If alpha,beta,gamma are the cube roots of p, then for any x,y,z (x alpha + y beta + z gamma)/(x beta + y gamma + z alpha =

If alpha,beta,gamma are the cube roots of p, then for any x,y,z (x alpha + y beta + z gamma)/(x beta + y gamma + z alpha =

If alpha,beta,gamma are the cube roots of p, then for any x,y,z (x alpha + y beta + z gamma)/(x beta + y gamma + z alpha =

If alpha,beta,gamma are the cube roots of p, then for any x,y,z(x alpha+y beta+z gamma)/(x beta+y gamma+z alpha)=

If alpha,beta,gamma are the cube roots of p(p<0) then for any x,y and z,quad (x+y beta+z gamma)/(x beta+y gamma+z alpha)=(1)/(2)(-1-i sqrt(3))(b)(1)/(2)(1+i sqrt(3))(1)/(2)(1-i sqrt(3)) (d) None of these

If alpha,beta,gamma are cube roots of of p<0 then for any real x,y,z;(x alpha+y beta+z gamma)/(x beta+y gamma+z alpha)=

If alpha, beta,gama are the cube roots of p, then for any x,y and z, frac{x(alpha)+y(beta)+z(gama)}{x(beta)+y(gama)+z(gama)} =

If p lt 0 and alpha, beta, gamma are cube roots of p then for any a,b and c show that (aalpha+b beta + cgamma)/(a beta+bgamma +calpha)=omega^(2) where omega is an imaginary cube root of 1.