If `log_(alpha)4 = gamma, log_(beta)alpha = - 1 and log_(1/2) beta = - 1` then the value of the expression `4 alpha^2 + beta^2 + gamma^2` equals to

If alpha/a+beta/b+gamma/c=1+i and a/alpha+b/beta+c/gamma=0 , then the value of alpha^2/a^2+beta^2/b^2+gamma^2/c^2 is equal to

If alpha, beta and gamma the roots of the equation x^(3) + 3x^(2) - 4x - 2 = 0. then find the values of the following expressions: (i) alpha ^(2) + beta^(2) + gamma^(2) (ii) alpha ^(3) + beta^(3) + gamma^(3) (iii) (1)/(alpha)+(1)/(beta)+(1)/(gamma)

If alpha, beta and gamma the roots of the equation x^(3) + 3x^(2) - 4x - 2 = 0. then find the values of the following expressions: (i) alpha ^(2) + beta^(2) + gamma^(2) (ii) alpha ^(3) + beta^(3) + gamma^(3) (iii) (1)/(alpha)+(1)/(beta)+(1)/(gamma)

If alpha, beta and gamma the roots of the equation x^(3) + 3x^(2) - 4x - 2 = 0. then find the values of the following expressions: (i) alpha ^(2) + beta^(2) + gamma^(2) (ii) alpha ^(3) + beta^(3) + gamma^(3) (iii) (1)/(alpha)+(1)/(beta)+(1)/(gamma)

If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is :

If log_(6)15 = alpha, log_(12)18= beta and log_(25)24 = gamma , then prove that gamma = (5 - beta)/(2(alphabeta+alpha-2beta+1))

If the area of the bounded region R= {(x,y): "max" {0, log_(e)x} le y le 2^(x), (1)/(2) le x le 2} is alpha (log_(e)2)^(-1) + beta (log_(e )2) +gamma , then the value of (alpha +beta-2gamma)^(2) is equal to

If alpha,beta,gamma are such that alpha+beta+gamma =4, alpha^2+beta^2+gamma^2 =6, alpha^3+beta^3+gamma^3 =8, then the value of [alpha^4+beta^4+gamma^4] must be equal to (where[.] denotes the greatest integer function)