Question

If a+b+c=0 prove that a3+b3+c3–3abc=0

Answer 1

Identity:

a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 +b^2 +c^2 - 2ab -2bc- 2ca)

if a+b+c=0,                    = 0 *(a^2 +b^2 + c^2 -2ab-2bc-2ca)

a^3 +b^3 +c^3 -3abc    = 0

a^3+b^3+c^3                 = 3abc

hence proved.