Question

If $a+b+c=0$, then find $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}$

• A. $3$
• B. $2$
• C. $1$
• D. $6$

Answer 1

The correct option is A $3$

If $a+b+c=0$, then $a^3+b^3+c^3=3abc$
$\therefore \frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}=\frac{a^3}{abc}+\frac{b^3}{abc}+\frac{c^3}{abc}=\frac{a^3+b^3+c^3}{abc}=\frac{3abc}{abc}=3$