Question

If a + 2b + c = 0; then show that:
$a^3+8b^3+c^3=6abc$.

Answer 1

Given, $a+2b+c=0$
We know that
$a^3+b^3+c^3=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)+3abc$
If $a+b+c=0$, then,
$a^3+b^3+c^3=3abc$
Here, $a=a$, $b=2b$ and $c=c$,
Thus,
$a^3+(2b{)}^3+c^3=3(a\left)\right(2b\left)\right(c)=6abc$
$=>$L.H.S=R.H.S