If `alpha` be a root of equation `x^2+x+1=0` then find the vlaue of `(alpha+ 1/alpha)+(alpha^2+1/alpha^2)^2+(alpha^3+1/alpha^3)^2+…+(alpha^6+1/alpha^6)^2`

If alpha is root of equation f(x)=0 then the value of (alpha+ 1/alpha)^2+(alpha^2+ 1/alpha^2)^2+(alpha^3+1/alpha^3)+………+(alpha^6+ 1/alpha^6)^2 is (A) 18 (B) 54 (C) 6 (D) 12

If alpha and beta are the roots of equation 6x^(2)+x-2=0 , find the value of (alpha)/(beta)+(beta)/(alpha) :

If alpha,beta are roots of the equation x^(2)-px+q=0, then find the value of (i)alpha^(2)(alpha^(2)beta^(-1)-beta)+beta^(2)(beta^(2)alpha^(-1)-alpha)

If alpha be a root of the equation, 4 x^2 + 2x - 1 =0 , then 4 alpha^3 - 3 alpha is other root.

If alpha is a root of x^(3)-x-1=0, compute the value of alpha^(10)+2 alpha^(8)-alpha^(7)-3 alpha^(6)-3 alpha^(5)+4 alpha^(4)+2 alpha^(3)-4 alpha^(2)-6 alpha

If alpha,beta be the roots of the equation 3x^(2)-6x+4=0, then find the value of ((alpha^(2))/(beta)+(beta^(2))/(alpha))+((alpha)/(beta)+(beta)/(alpha))+2((1)/(alpha)+(1)/(beta))+3 alpha beta

Match the following If alpha,beta are the roots of the equation x^2-4x+1=0, then Find the value of: 1- alpha^2+beta^2 , 2- alpha^3+beta^3 , 3- |alpha-beta| , 4- 1/alpha+1/beta

If alpha is a root of x^(4) + x^(2) - 1 = 0 , the value of (alpha^(6) + 2 alpha^(4))^(2012) is

If alpha be a root of the equation,4x^(2)+2x-1=0, then 4 alpha^(3)-3 alpha is other root.