If `x+y=z` prove that `x^(3)+y^(3)+3xyz=z^(3)`

If x + y + z = 0 , then prove that x^(3)+y^(3)+z^(3)= 3xyz

If x+y+z=0 show that x^(3)+y^(3)+z^(3)=3xyz .

If x + y + z = xyz , prove that (3x -x^(3))/ (1-3x^(2)) + (3y -y^(3))/(1- 3y^(2)) +(3z -z^(3))/(1- 3z^(2)) = (3x -x^(3))/(1-3x)^(2) * (3y- y^(3))/(1-3x)^(2)* (3z- z^(3))/(1-3z)^(2) .

If quad x+y+z=0 show that x^(3)+y^(3)+z^(3)=3xyz

x+y+z=0 Show that x^(3)+y^(2)+z^(3)=3xyz

If x+y+z=xyz , prove that (3x-x^3)/(1-3x^2)+(3y-y^3)/(1-3y^2)+(3z-z^3)/(1-3z^2) = (3x-x^3)/(1-3x^2) cdot(3y-y^3)/(1-3y^2)cdot(3z-z^3)/(1-3z^2)

If x +y+ z=xyz , prove that : (3x-x^3)/(1-3x^2)+ (3y-y^3)/(1-3y^2)+(3z-z^3)/(1-3z^2)= (3x-x^3)/(1-3x^2). (3y-y^3)/(1-3y^2).(3z-z^3)/(1-3z^2) .

If x+y+z=0 and (x^(3)+y^(3))/(xyz)=(y^(3)+z^(3))/(xyz)=(x^(3)+z^(3))/(xyz)=a , then which of the following can be 'a'?