Question

If a+b+c=0, the $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}$ is equal to _____.

• A. 0
• B. 1
• C. 3
• D. 2

Answer 1

Answer: (C)

3

Using the formula, a^3 + b^3 + c^3 = (a + b + c) (a^2 + b^2 + c^2 ab bc ca) + 3abc
If a+b+c=0,
then a^3 + b^3 + c^3 = 3abc
$\frac{a^3+b^3+c^3}{abc}=3$
$\frac{a^3}{abc}+\frac{b^3}{abc}+\frac{c^3}{abc}=3$
$\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}=3$
Answer (C) 3