" tet "A=[[0,2],[0,0]]" and "(A+h)^(100)-100A=[[alpha,beta],[gamma,delta]]," then "alpha+beta+gamma+delta=......

Let A=[(0,2),(0,0)]and (A+1)^100 -100A=[(alpha,beta),(gamma,delta)], then alpha+beta+gamma+delta=...

Let A=[(0,2),(0,0)]and (A+1)^100 -100A=[(alpha,beta),(gamma,delta)], then alpha+beta+gamma+delta=...

alpha,beta are the roots of the equation x^(2)-4x+lambda=0, and gamma,delta are the roots of the equation x^(2)-64x+mu=0. If alpha,beta,gamma,delta form an increasing G.P,find the values of alpha,beta,gamma,delta

If |((beta+gamma-alpha -delta)^4 , (beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4, (gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4, (alpha + beta-gamma-delta)^2,1)|=-k(alpha -beta)(alpha -gamma)(alpha-delta)(beta-gamma)(beta-delta)(gamma-delta) , then the value of (k)^(1//2) is ____

Prove that |{:(2,alpha+beta+gamma+delta,alphabeta +gammadelta),(alpha+beta+gamma+delta,2(alpha+beta)(gamma+delta),alphabeta(gamma+delta)+gammadelta(alpha+beta)),(alphabeta+gammadelta,alphabeta(gamma+delta)+gammadelta(alpha+beta),2alphabetagamma delta):}| =0

If alpha, beta, gamma and delta are the roots of the equation x ^(4) -bx -3 =0, then an equation whose roots are (alpha +beta+gamma)/(delta^(2)), (alpha +beta+delta)/(gamma^(2)), (alpha +delta+gamma)/(beta^(2)), and (delta +beta+gamma)/(alpha^(2)), is:

If alpha, beta, gamma and delta are the roots of the equation x ^(4) -bx -3 =0, then an equation whose roots are (alpha +beta+gamma)/(delta^(2)), (alpha +beta+delta)/(gamma^(2)), (alpha +delta+gamma)/(beta^(2)), and (delta +beta+gamma)/(alpha^(2)), is:

Prove that |{:(2,,alpha+beta+gamma+delta,,alphabeta+gammadelta),(alpha+beta+gamma+delta,,2(alpha+beta)(gamma+delta),,alphabeta(gamma+delta)+gammadelta(alpha+beta)),(alphabeta+gammadelta,,alphabeta(gamma+delta)+gammadelta(alpha+beta),,2alphabetagammadelta):}|=0

Prove that |2 alpha+beta+gamma+delta alphabeta+gammadelta alpha+beta+gamma+delta 2(alpha+beta)(gamma+delta) alphabeta(gamma+delta)+gammadelta(alpha+beta) alphabeta+gammadeltaalphabeta(gamma+delta)+gammadelta(alpha+beta)2alphabetagammadelta|=0