If \( a + b + c = 0 \), then the value of: \[ \frac{a^2}{bc} + \frac{b^2}{ac} + \frac{c^2}{ab} \] is:
\[ \frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} = \frac{a^3 + b^3 + c^3}{abc} \] \[ = \frac{a^3 + b^3 + c^3 - 3abc + 3abc}{abc} \] \[ = \frac{(a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)}{abc} + 3 \] \[ = 3 \]
Reinforce your conceptual grasp with related questions from NIMCET 2020:
If \( 15\\ 8 + 15\\ 7 = n\\ r \)
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