`P_n=alpha^n+beta^n , alpha +beta=1 , alpha*beta=-1 , P_(n-1)=11 ,P_(n+1)=29 , then P_(n)^2=`

| alpha alpha1 beta F|=(alpha-P)(beta-alpha)

Let alpha and beta be two real numbers such that alpha+beta=1 and alpha beta=-1 Let p_(n)=(alpha)^(n)+(beta)^(n), p_(n-1)=11 and p_(n+1)=29 for some integer n geq 1 Then, the value of p_(n)^(2) is

Let alpha and beta be the roots of the equation x^(2) -px+q =0 and V_(n) = alpha^(n) + beta^(n) , Show that V_(n+1) = pV_(n) -qV_(n-1) find V_(5)

If l,m,n, be the three positive roots of the equation x^(3)-ax^(2)+bx-48=0 , then the minimum value of (1)/(l)+(2)/(m)+(3)/(n) equals (alpha)/(beta) where alpha,beta in N , gcd(alpha,beta)=1 then alpha^(2)+beta^(2)=

if a_(n=(alpha^(n)-beta^(n))/(alpha-beta) where alpha and beta are roots of equation x^(2)-x-1=0 and b_(n)=a_(n+1)+a_(n-1) then

If tan(alpha+beta)=n tan(alpha-beta) then show that (n+1)sin2 beta=(n-1)sin2 alpha