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 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 is a root of the equation 4x ^2 +2x-1=0 then 4 alpha ^3 - 3 alpha is

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

Prove that |{: (1,alpha,alpha^2), (alpha,alpha^2, 1),(alpha^2, 1,alpha) :}|=-(1-alpha^3)^2

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

If alpha is a root of the equation 4x^(2)+2x-1=0 then the other root is given by O -2 alpha-1 O 4 alpha^(2)+alpha-1 O 4 alpha^(3)-3 alpha O 4 alpha^(2)-3 alpha

If alpha is a non real root of the equation x^(6)-1=0 then (alpha^(2)+alpha^(3)+alpha^(4)+alpha^(5))/(alpha+1)