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 |[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 xneynez" and " |{:(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3)):}|=0, then xyz =

If tan^(-1) x + tan^(-1) y - tan^(-1) z = 0 , then prove that : x+ y + xyz = z .

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 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

(x+ (1)/(y)) = (y+ (1)/(z))= (z + (1)/(x)) and (x ne y ne z) find xyz= ?