Let `alpha,beta,gamma` be roots of the cubic `x^(3)+ax+a=0` where `a in R-{0},` then the value of `(a+beta)^(-1)+(beta+gamma)^(-1)+(gamma+a)^(-1)` is equal to

If alpha,beta,gamma are the roots of he euation x^(3)+4x+1=0 ,then find the value of (alpha+beta)^(-1)+(beta+gamma)^(-1)+(gamma+alpha)^(-1)

If alpha, beta, gamma are the roots of the equation x^(3) + x + 1 = 0 , then the value of alpha^(3) + beta^(3) + gamma^(3) , is

Let alpha,beta,gamma be the roots of the equation 8x^(3)+1001x+2008=0 then the value (alpha+beta)^(3)+(beta+gamma)^(3)+(gamma+alpha)^(3) is

If alpha,beta,gamma are the roots of the equation x^(3)+px^(2)+qx+r=0, then the value of (alpha-(1)/(beta gamma))(beta-(1)/(gamma alpha))(gamma-(1)/(alpha beta)) is

If roots of x ^(3)+2x ^(2) +1=0 are alpha, beta and gamma, then the value of (alpha beta )^(3)+ (beta gamma ) ^(3) + (alpha gamma )^(3), is:

If alpha,beta,gamma are the roots of the equation x^(3)+px^(2)+qx+r=0, then find he value of (alpha-(1)/(beta gamma))(beta-(1)/(gamma alpha))(gamma-(1)/(alpha beta))

If alpha, beta and gamma are the roots of the cubic equation (x-1)(x^(2) + x + 3)=0 , then the value of alpha^(3) + beta^(3) + gamma^(3) is: