Given that
\[ \frac{ \color{red}{a}}{\color{blue}{b}+\color{orange}{c}} + \frac{\color{blue}{b}} {\color{red}{a}+\color{orange}{c}} + \frac{ \color{orange}{c}}{\color{red}{a}+\color{blue}{b}} = 1, \]
find the value of
\[\large \frac{ \color{red}{a}^2}{\color{blue}{b}+\color{orange}{c}} + \frac{ \color{blue}{b}^2}{\color{red}{a}+\color{orange}{c}} + \frac{ \color{orange}{c}^2} { \color{red}{a}+\color{blue}{b}}. \]
by
Sahil Goel
