`|[y+z, x, y],[z+x, z, x],[x+y, y, z]|=...`

Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are nonzero real number, is equal to x y z b. 2x y z c. 3x y z d. 4x y z

Prove that Det [[x + y + 2z, x, y], [z, y + z + 2x, y], [z, x, z + x + 2y]] = 2 (x + y + z) ^ 3

Let x, y, z are distinct cube roots of unity and the value of |[x,y-z,z-y],[x-z,y,z-x],[x-y,y-x,z]|=K then |K|

Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)

Prove that |[x+y, y+z, z+x] , [z+x, x+y, y+z] , [y+z, z+x, x+y]|=2|[x,y,z] , [z,x,y] , [y,z,x]|

Prove: |(y+z, z, y),( z, z+x,x),( y, x,x+y)|=4\ x y z

|[z+y,x,x] , [y,z+x,y] , [z,z,x+y]|=

y+z,x,yz+y,z,xx+y,y,z]|=(x+y+z)(x-z)^(2)

A(x, y, z)=" min. "(x+y, y+z, z+x) B(x, y, z)="max "(x-y, y-z, z-x) C(x, y, z)=" max"(A(x, y, z), B(x, y, z)) D(x, y, z)=" min "(A(x, y, z), B(x, y, z)) The value of C(1, 2, 3) is :

A(x, y, z)=" min. "(x+y, y+z, z+x) B(x, y, z)="max "(x-y, y-z, z-x) C(x, y, z)=" max"(A(x, y, z), B(x, y, z)) D(x, y, z)=" min "(A(x, y, z), B(x, y, z)) Whgat is the value D(1, 2, C(0, 1, 2)) ?