If x + y + z = 0 , show that` | [ 1 , 1 , 1 ] , [ x , y , z ] , [ x^3 , y^3 , z^3 ] |` = 0

Prove that |[x,y,z] , [x^2, y^2, z^2] , [yz, zx, xy]| = |[1,1,1] , [x^2, y^2, z^2] , [x^3, y^3, z^3]|

If x + y + z = 0 , then what is (y+z-x)^(3) + (z+x-y)^(3) + (x+y-z)^(3) equal to ?

2x-3z + w = 1x-y + 2w = 1-3y + z + w = 1x + y + z = 1

Find the value of (( x -y )^3 + ( y - z )^3 + ( z - x )^3 )/ (9 ( x - y )( y - z ) ( z - x )) 1 . 0 2 . 1/9 3 . 1/3 4. 1

Without expanding as far as possible, prove that |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}| = (x-y)(y-z)(z-x)(x+y+z) .

Prove that : |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}|=(x-y)(y-z)(x+y+z)

If x^(1//3) + y^(1//3) + z^(1//3) = 0 , then the value of (x + y + z)^3 is :