Question

if x+y+z-=0 show that x3+y3+z2=3xyz

Answer 1

Answer:

x+y+z=0

x+y=-z

(x+y)^3=(-z)^3 (cubing both sides)

x^3+y^3+3xy(x+y)=-z^3

x^3+y^3-3xyz=-z^3. (x+y=-z)

x^3+y^3+z^3=3xyz

Hence Proved