If `alpha,beta` are the non-real cube roots of `3` then `alpha^(6)+beta^(6)=`

If alpha, beta, gamma are the cube roots of 8 , then |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|=

If alpha and beta are the complex cube roots of unity, show that alpha^4+beta^4 + alpha^-1 beta^-1 = 0.

If alpha , beta are the roots of ax^(2) + bx +c=0 , then (alpha^(3) + beta^(3))/(alpha^(-3) + beta^(-3)) is equal to :

If alpha and beta are the complex cube roots of unity, then prove that (1 + alpha) (1 + beta) (1 + alpha)^(2) (1+ beta)^(2)=1

(i) If alpha , beta be the imaginary cube root of unity, then show that alpha^4+beta^4+alpha^-1beta^-1=0

If alpha, beta are the rootsof 6x^(2)-4sqrt2 x-3=0 , then alpha^(2)beta+alpha beta^(2) is

If alpha, beta are the roots of x^(2) + x + 3=0 then 5alpha+alpha^(4)+ alpha^(3)+ 3alpha^(2)+ 5beta+3=

If alpha, beta are the roots of x^(2)-px+q=0 then (alpha+beta)x-(alpha^(2)+beta^(2))(x^(2))/(2)+(alpha^(3)+beta^(3))(x^(3))/(3)-….oo=

If alpha , beta are the roots of ax ^2 + bx +c=0 then alpha ^5 beta ^8 + alpha^8 beta ^5=

If alpha , beta are the roots of x^2 +x+1=0 then alpha beta + beta alpha =