Question

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

Answer 1

$\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}=\frac{a^3+b^3+c^3}{abc}$

if $(a+b+c)=0$

$\Rightarrow a^3+b^3+c^3=3abc$

$\therefore \frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}=3$