Question

If a+b+c=0, then show that a^3+b^3+c^3=3abc

Answer 1

Find a³+b³+c³ = 3abc

a+b+c = 0

a+b = -c

(a+b)³ = (-c)³

a³+b³+3ab(a+b) = -c³

a³+c³ +3ab(-c) = -c³                                      [ (a+b) = -c ]

a³+b³-3abc = -c³

a³+b³+c³ = 3abc