Question : If $a+b+c=0$, then the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{a b}$ is:
Option 1: 1
Option 2: 3
Option 3: - 1
Option 4: 0
Answer (1)
8th Jan, 2024
Correct Answer: 3
Solution :
$a+b+c=0$
$a^3+b^3+c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$
⇒ $a^3+b^3+c^3 - 3abc = 0$
⇒ $a^3+b^3+c^3 = 3abc$
⇒ $\frac{a^3+b^3+c^3}{abc} = 3$
⇒ $\frac{a^2}{bc} + \frac{b^2}{ac} + \frac{c^2}{ab} = 3$
Hence, the correct answer is 3.
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