Question

If $a+b+c=0$, then what is the value of $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}$?

• A. $-3$
• B. $0$
• C. $1$
• D. $3$

Answer 1

The correct option is D $3$

Given : $a+b+c=0$

To find : $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}$

we have been given that

$a+b+c=0$

we know that,

If $a+b+c=0$ than $a^3+b^3+c^3=3abc...\left(1\right)$

We need to find

$\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}...\left(2\right)$

taking the LCM of eq(2)

Therefore, $\frac{a^3+b^3+c^3}{abc}...\left(3\right)$

from eq (1) and (3)

$\frac{a^3+b^3+c^3}{abc}\Rightarrow \frac{3abc}{abc}=3$

Therefore, $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}=3$