1.00.3" If "x_(2)B" are roots of the equation "x^(2)-2x+4n0,S*Ta^(2)+beta^(n)=2^(n+1)cos((n pi)/(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 the equation x^(2)-2x+4=0 Then 2^(n+1)cos backslash(n pi)/(3) is equal to

If alpha,beta are roots of the equation x^(2)-4x+8=0 then for any ninN,alpha^(2n)+beta^(2n)

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^2-2x+4=0 , find alpha^(n)+beta^(n) for (a) n=3k, k in N (b) n ne 3k, k in N

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

If x_(1),x_(2),x_(3),andx_(4) are the roots of the equations x^(4)-x^(3)sin2 beta+x^(2)cos2 beta-x cos beta-sin beta=0, prove that tan^(-1)x_(1)+tan^(-1)x_(2)+tan^(-1)x_(3)+tan^(-1)x_(4)=n pi+((pi)/(2))-beta, where n is an integer.

If alpha,beta are the roots of the equation, x^(2)-x-1=0 and S_(n)=2023 alpha^(n)+2024 beta^(n) ,then 2S_(12)=S_(11)+S_(10)