Prove that `|((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)|=-64(alpha-beta)(alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta)(gamma-delta)`

If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 Find the equations whose roots are (i) beta gamma +1/(alpha), gamma alpha+1/(beta), alpha beta+1/(gamma) (ii) (beta+gamma-alpha),(gamma+alpha-beta),(alpha+beta-gamma) Also find the valueof (beta+gamma-alpha)(gamma+alpha-beta)(alpha+beta-gamma)

Using properties of determinants in Exercise 11 to 15 prove that |{:(alpha,alpha^2,beta+gamma),(beta,beta^2,gamma+alpha),(gamma,gamma^2,alpha+beta):}|=(beta-gamma)(gamma-alpha)(alpha+beta+gamma)(alpha-beta)

The value of |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaalpha,gammaalpha'+gamma'alpha,gamma'alpha'),(alphabeta,alphabeta'+alpha'beta,alpha'beta'):}| is

If a matricx [{:(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma):}] is a orthogonal matrix then ………

Explain alpha beta and gamma rays

Show that the lines (x-a+d)/(alpha- delta)=(y-a)/(alpha)=(z-a-d)/(alpha+delta) and (x-b+c)/(beta-gamma)=(y-b)/(beta)=(z-b-c)/(beta+gamma) are coplanar.

If cos^(-1)alpha+cos^(-1)beta+cos^(-1)gamma=3pi , then alpha(beta+gamma)+beta(gamma+alpha)+gamma(alpha+beta) equals to ______

If alpha,beta,gamma are the roots of x^(3)+2x^(2)-x-3=0 The value of |{:(alpha, beta ,gamma),(gamma,alpha ,beta),(beta,gamma ,alpha):}| is equal to

If p''(x) has real roots alpha,beta,gamma . Then , [alpha]+[beta]+[gamma] is