if `alpha, beta, gamma` are roots of `x^3-3x^2+3x+7=0`, then find `(alpha-1)/(beta-1)+(beta-1)/(gamma-1)+(gamma-1)/(alpha-1)`

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+p x^2+q x+r=0, then find he value of (alpha-1/(betagamma))(beta-1/(gammaalpha))(gamma-1/(alphabeta)) .

If alpha,beta,gamma are the roots of x^3+ax+b =0, then the value of alpha^3+beta^3+gamma^3

If alpha, beta, gamma are the roots of x^3 + px + q = 0 , then alpha beta gamma = ___________ .

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

If alpha, beta. gamma are the roots of x^3 + px^2 + q = 0, where q=0, ther Delta=[(1/alpha,1/beta,1/gamma),(1/beta,1/gamma,1/alpha),(1/gamma,1/alpha,1/beta)] equals

If alpha,beta,gamma are the angles of a triangle and system of equations cos(alpha-beta)x+cos(beta-gamma)y+cos(gamma-alpha)z=0 cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0 sin(alpha+beta)x+sin(beta+gamma)y+sin(gamma+alpha)z=0 has non-trivial solutions, then triangle is necessarily a. equilateral b. isosceles c. right angled "" d. acute angled

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 different from 1 and are the roots of a x^3+b x^2+c x+d=0a n d(beta-gamma)(gamma-alpha)(alpha-beta)=(25)/2 , then prove that |alpha/(1-alpha)beta/(1-beta)gamma/(1-gamma)alphabetagammaalpha^2beta^2gamma^2|=(25 d)/(2(a+b+c+d))

If alpha , beta , gamma are the roots of the equation px^3 - qx + r = 0 , then the value of alpha + beta + gamma is