If x, y, z are different and `Delta=|[x, x^2, 1+x^3],[y, y^2, 1+y^3],[z, z^2, 1+z^3]|=0` then show that `1+xyz=0`

If x,y,z are different and Delta=det[[x,x^(2),1+x^(3)y,y^(2),1+y^(3)z,z^(2),1+z^(3)]]=0 then show that 1+xyz=0]|

If x,y,z are different and Delta=det[[x,x^(2),1+x^(3)y,y^(2),1+y^(3)z,z^(2),1+z^(3)]]=0, then prove that 1+xyz=0,

If x,y,z are different and Delta=|{:(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3)):}|=0 , show that : (i) 1+xyz=0 (ii) xyz=-1

If x,y,z are different and Delta=det[[x,x^(2),x^(3)-1y,y^(2),y^(3)-1z,z^(2),z^(3)-1]]=0, then using properties of determinants,show that xyz=1

If |{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^2,1+z^3):}|=0 then relation of x,y and z is

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a.1 b. 2 c. -1 d. 2

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

Prove that [[x, x^2 , 1+px^3], [y, y^2, 1+py^3] ,[z, z^2, 1+pz^3]] = (1+pxyz)(x-y)(y-z)(z-x)

If x,y,z are distinct and |(x, x(x^2+1), x+1),(y,y(y^2+1), y+1),(z, z(z^2+1), z+1)|=0 then (A) xyz=0 (B) x+y+z=0 (C) xy+yz+zx=0 (D) x^2+y^2+z^2=1