Question : If $a, b, c$ are all non-zero and $a+b+c=0$, then find the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{ab}$.
Option 1: $3$
Option 2: $4$
Option 3: $1$
Option 4: $\frac{1}{2}$
Answer (1)
23rd Jan, 2024
Correct Answer: $3$
Solution :
Given: $a+b+c=0$
According to the question,
$a^3+b^3+c^3=3abc$
Dividing both sides by $abc$, we get
$\frac{a^3}{abc}+\frac{b^3}{abc}+\frac{c^3}{abc}=\frac{3abc}{abc}$
⇒ $\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}=3$
Hence, the correct answer is 3.
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