If `alpha` and `beta` are the roots of the equation `x^2-2x+4=0`, prove that `alpha^n+beta^n=2^(n+1)cos(npi/3)`

If alpha and beta are the roots of the equation x^(2)-2x+4=0, prove that alpha^(n)+beta^(n)=2^(n+1)cos(n(pi)/(3))

If alpha and beta are the roots of x^2 - 2x + 4 = 0 , Prove that alpha^n+beta^n = 2^(n+1) cos((npi)/3)

If alpha and beta are the roots of the equation x^(2)-ax+b=0 and A_(n)=alpha^(n)+beta^(n)

If alpha,beta are the roots of the equation x^2-2x+4=0 , find alpha^(n)+beta^(n) for (a) n=3k, k in N

If alpha, beta are the roots of the equation x^(2) + x + 1 = 0 then prove that alpha^(4) + beta^(4) + alpha^(-1) beta^(-1) = 0 .