Question

If $a+b+c=0$ then find the value of $a^3+b^3+c^3$.

Answer 1

Given,

$a+b+c=0$

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

Now cubing both sides we get,

$(a^3+b^3+3ab(-c)=-c^3$ [ Using (1)]

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