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

If |(x, x^2, x^3 +1), (y, y^2, y^3+1), (z, z^2, z^3+1)| = 0 and x ,y and z are not equal to any other, prove 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 cos^-1 x+cos^-1 y+cos^-1 z=pi and x+y+z= 3/2, then prove that x=y=z

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

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!=y!=z and |x^(2)1+x^(3)yy^(2)1+y^(3)zz^(2)1+z^(3)|=0, then prove that xyz=-1

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]|