Question

State true or false:

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

• A. True
• B. False

Answer 1

The correct option is A True

We know that,
$(a+b+c{)}^3=a^3+b^3+c^3+3[(a+b+c)(ab+bc+ca)-abc]$
If $a+b+c=0$ then,
$a^3+b^3+c^3=3abc$
Now,
$a+2b+c=0$
L.H.S$=a^3+8b^3+c^3$
$=3\left(a\right)\left(2b\right)\left(c\right)$[Since $a+2b+c=0$]
$=6abc$