Question

If non - zero a, b, c are such that a + b + c = 0, then the value of \(\frac{a^2}{bc} + \frac{b^2}{ac} + \frac{c^2}{ab}\) is
1. 3
2. 2
3. -3
4. 0

Answer 1

Correct Answer - Option 1 : 3

Given:

a + b + c = 0

Formula Used:

If a + b + c = 0 then

a3 +b3 + c3 = 3abc

Calculation:

\(\frac{a^2}{bc} + \frac{b^2}{ac} + \frac{c^2}{ab}\)

\(=\frac{a^3+b^3+c^3}{abc}\)

Substitute the value a3 +b3 + c3 = 3abc in the given expression

\(\Rightarrow \frac{{{a^3}\; + \; {b^3}\; + \;{c^3}}}{{abc}} = \frac{{3abc}}{abc}\)

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

∴ The correct answer is 1