Let `beta ` be a real number .Consider the matrix
`A ={:((beta,0,1),(2,1,-2),(3,1,-2)):}`
If `A^(7) - (beta -1)A^(6) -betaA^(5)` is a singular , then the value of `9 beta ` is _______.

If the points (5,-2,7),(2,2,beta)and(-1,6,-1) are collinear, then the value of beta is

Let alpha , beta be two real numbers satisfying the following relations alpha^(2)+beta^(2)=5 , 3(alpha^(5)+beta^(5))=11(alpha^(3)+beta^(3)) Possible value of alpha + beta is

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

Let alpha,beta be two real numbers satisfying the following relations alpha^(2)+beta^(2)=5,3(alpha^(5)+beta^(5))=11(alpha^(3)+beta^(3))1 Possible value of alpha beta is

Let alpha, beta be the roots of equation x ^ 2 - x + 1 = 0 and the matrix A = (1 ) /(sqrt3 ) |{:(1,,1,,1),(1,,alpha,,alpha ^2),(1,,beta,,-beta^ 2):}| , the value of det (A. A^T) is

Let -(1)/(6) beta_(1) and alpha_(2)>beta_(2), then alpha_(1)+beta_(2) equals

If P(5,6,-1),Q (2,-7,beta ) and R (-1,-20,7) are collinear , then beta =

Let beta(n)=int_(0)^(n pi)sqrt(1-sin t)dt. Find the value of beta(2)-beta(1)

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