सिद्ध कीजिए की `|{:(,1,x+alpha,y+z-alpha),(,1,y+beta,z+x-beta),(,1,z+y,x+y-gamma):}|=0`

Prove that |{:(1,x+alpha,y+z-alpha),(1,t+beta,+x-beta),(1,z+gamma,x+y-gamma):}|=0

Let alpha and beta be the roots of the equation x^(2) + x + 1 = 0 . Then, for y ne 0 in R. |{:(y+1, alpha,beta), (alpha, y+beta, 1),(beta, 1, y+alpha):}| is

If alpha,beta,gamma are the cube roots of p, then for any x,y,z(x alpha+y beta+z gamma)/(x beta+y gamma+z alpha)=

If alpha,beta,gamma are the cube roots of p then for any x,y and z(x alpha+y beta+z gamma)/(x beta+y gamma+z alpha) is

Let alpha and beta be the roots of the equation x^(2)+x+1=0. Then for y ne 0 in R, |(y+1,alpha,beta),(alpha,y+beta,1),(beta,1,y+alpha)| is equal to :

Consider the system of equations : x + y + z = 0 alpha x + beta y + gamma z = 0 alpha^(2) x + beta^(2) y + gamma^(2) z = 0 then the system of equations has

In the radioacitve decay ._(Z)X^(A) rarr ._(z + 1)Y^(A) rarr ._(z - 1)^(A - 4) rarr ._(z - 1)Z^(*A - 4) The sequence of emission is a. alpha, beta, gamma b. gamma, alpha, beta c. beta, alpha, gamma c. beta, gamma, alpha

If =(beta-gamma)(alpha-delta),y=(gamma-alpha)(beta-delta),z=(alpha-beta)(gamma-delta) ,then value of x^(3)+y^(3)+z^(3)-3xyz is