Question

If $a+b+c=0$ then $(a^3+b^3+c^3)÷abc$ is equal to

• A. 1
• B. 2
• C. 3
• D. 9

Answer 1

The correct option is C 3

$a+b+c=0\Rightarrow a+b=-c\Rightarrow {(a+b)}^3={(-c)}^3\Rightarrow a^3+b^3+3ab(a+b)={-c}^3\Rightarrow a^3+b^3+c^3+3ab(-c)=0\Rightarrow a^3+b^3+c^3=3abc\Rightarrow \frac{a^3+b^3+c^3}{abc}=3$