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

Explanation

Given that– a + b + c = 0 so a³ + b³ + c³ = 3abc .................(i) Now $$ \frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} $$ $$ = \frac{a^3}{abc} + \frac{b^3}{bca} + \frac{c^3}{cab} $$ $$ = \frac{a^3 + b^3 + c^3}{abc} $$ from equation (i) $$ \frac{3abc}{abc} $$ $$ \frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} = 3 $$