Question

If $a+b+c=0$, then $a^3+b^3+c^3=kabc$, the value of '$k$' is

Answer 1

Given,

$a+b+c=0$.......(1).

or, $a+b=-c$

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

Comparing this with the given problem we get, $k=3$.