Question

if x + y + z = 0 then prove x³ +y³+z³=3xy

Answer 1

x+y+z=0
x+y= -z
(x+y)^3 = (-z)^3
x^3 +y^3 +3xy(x+y)= -z^3
x^3+y^3+z^3=-3xy(x+y)
x^3+y^3+z^3= -3xy *(-z)
x^3+y^3+z^3=3xyz

Answer 2

x^3 +y^3 +z^3 - 3xyz = (x+y+z)(x+y+z-ab-bc-ca)
If x+y+z=0,
x^3+y^3+z^3- 3xyz =0
x^3+y^3+z^3 =3xyz