Question

If $a+b+c=0$, then the value of
$-(\frac{a^2+b^2+c^2}{bc+ca+ab})$ is....

• A. $2$
• B. $-2$
• C. $-1$
• D. $3$

Answer 1

The correct option is B $-2$

${(a+b+c)}^2=0$
$\Rightarrow a^2+b^2+c^2+2(ab+bc+ca)=0$
$a^2+b^2+c^2=-2(ab+bc+ca)$
$\Rightarrow \frac{a^2+b^2+c^2}{bc+ca+ab}=-2$