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

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

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

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

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

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

If alpha, beta, gamma are the roots of the equation 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

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