Question:
If $a, b, c$ are all nonzero and $a+b+c=0$, prove that $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=3$.
Solution:
$a+b+c=0 \Rightarrow a^{3}+b^{3}+c^{3}=3 a b c$
Thus, we have:
$\left(\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}\right)=\frac{a^{3}+b^{3}+c^{3}}{a b c}$
$=\frac{3 a b c}{a b c}$
$=3$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.