Question 125
Let $a$, $b$, $c$ be real numbers such that
$$
\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} = 1.
$$
Determine all values that the following expression can take:
$$
\frac{a^{2}}{b+c} + \frac{b^{2}}{c+a} + \frac{c^{2}}{a+b}.
$$
$$
\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} = 1.
$$
Determine all values that the following expression can take:
$$
\frac{a^{2}}{b+c} + \frac{b^{2}}{c+a} + \frac{c^{2}}{a+b}.
$$