Question

If $a+b+c=0$ then prove that $a^3+b^3+c^3=3abc$.

Answer 1

Given $a+b+c=0$

or, $a+b=-c$.......(1).

Now cubing both sides we get,

$(a+b{)}^3=-c^3$

or, $a^3+b^3+3ab(a+b)=-c^3$

or, $a^3+b^3-3abc=-c^3$ [ Using (1)]

or, $a^3+b^3+c^3=3abc$.