If for the matrix , `A = [(1,-alpha),(alpha, beta)], A A^T = I_2`, then the value of `alpha^4 + beta^4` is:

If A=[(1,-alpha),(alpha,beta)] and A A^T=I .Then find the value of alpha and beta

If alpha and beta are connected by the relations alpha^(2)+alpha=1 and beta^(2)+beta=1, then the value of alpha^(2)+beta^(2) is eqal to

If alpha^(2)=5 alpha-3 beta^(2)=5 beta-3 then the value of (alpha)/(beta)+(beta)/(alpha) is

If alpha, beta are roots of x^(2)-2x-1=0 , then value of 5alpha^(4)+12beta^(3) is

If 4 sin 27^(@)=sqrt(alpha)-sqrt(beta) , then the value of (alpha+beta-alpha beta+2)^(4) must be

If alpha and beta are the roots of 4x^(2) + 3x +7 =0 then the value of 1/alpha + 1/beta is

If alpha and beta are the zeroes of x^2 - 8x + 1 , then the value of 1/alpha +1/beta - alpha beta is :

If the coefficient of x^(14) in the expansion of (4x^(2)+x+1)^(8) is alpha xx4^(beta), then the value of (alpha+beta) is equal to (where alpha and beta are relatively prime to each other and beta>1)

If sin(alpha+beta)=(4)/(5), sin(alpha-beta)=(5)/(13) , find the value of tan 2alpha :