If a + b + c = 0, then find a^2/bc + b^2/ca + c^2/ab.

Question

If a + b + c = 0, then find \(\frac{a^2}{bc} +\frac{b^2}{ca}+\frac{c^2}{ab}.\)

Answer 1

If a + b+ c = 0, then a³ + b³ + c³ = 3abc

∴ \(\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab} =\frac{a^3}{abc}+\frac{b^3}{abc}+\frac{c^3}{abc}=\frac{a^+b^3+c^3}{abc}=\frac{0}{abc} = 0.\)