If `S_r=alpha^r+beta^r+gamma^r` then show that `|(S_2, S_1, S_2), (S_1, S_2, S_3), (S_2, S_3, S_4)| =(alpha-beta)^2 (beta-gamma)^2(gamma-alpha)^2`

If S_r = alpha^r + beta^r + gamma^r then show that |[S_0,S_1,S_2],[S_1,S_2,S_3],[S_2,S_3,S_4]| = (alpha-beta)^2(beta-gamma)^2(gamma-alpha)^2

If S_r = alpha^r + beta^r + gamma^r then show that |[S_0,S_1,S_2],[S_1,S_2,S_3],[S_2,S_3,S_4]| = (alpha-beta)^2(beta-gamma)^2(gamma-alpha)^2

If S_(r)=alpha^(r)+beta^(r)+gamma^(r) then show that det[[S_(0),S_(1),S_(2)S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)det[[S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)

|{:(1,alpha,alpha^2),(1,beta,beta^2),(1,gamma,gamma^2):}|=(alpha-beta)(beta-gamma)(gamma-alpha)

If alpha, beta , gamma are the zeros of the polynomial x^(3) - px^(2) + qx - r then 1/(alpha beta) + 1/(beta gamma) + 1/(gamma alpha) = …………..

Show that |[1,alpha,alpha^2],[1,beta,beta^2],[1,gamma,gamma^2]|=(alpha-beta)(beta-gamma)(gamma-alpha)

Show that | (1,1,1), (alpha ^ 2, beta ^ 2, gamma ^ 2), (alpha ^ 3, beta ^ 3, gamma ^ 3) | = (alpha-beta) (beta-gamma) (gamma-alpha) (alphabeta + betagamma + gammaalpha) |