The Total solution for NCERT class 6-12
If x+y+z= 0, show that x3+y3+z3 = 3xyz.
We know that,
x3+y3+z3-3xyz = (x +y+z)(x2+y2+z2–xy–yz–xz)
Now, according to the question, let (x+y+z) = 0,
then, x3+y3+z3 -3xyz =(0)(x2+y2+z2–xy–yz–xz)
⇒ x3+y3+z3–3xyz= 0
⇒ x3+y3+z3 =3xyz
Hence Proved