If \(a+b+c=0\), then find the value of \(\displaystyle\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}\).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3
If three numbers add up to zero, \(a^3+b^3+c^3=3abc\). The given expression has exactly \(a^3+b^3+c^3\) over \(abc\).
Common denominator \(abc\): \(\displaystyle\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}=\frac{a^3+b^3+c^3}{abc}\)
\(a+b+c=0\), so \(a^3+b^3+c^3=3abc\)
Value \(\displaystyle=\frac{3abc}{abc}=3\)