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 which the following expression can take : $$\frac{a^2}{b + c} + \frac{b^2}{c + a} + \frac{c^2}{a + b}.$$
Source: Switzerland - 2015 Swiss MO Final Round p7
Tags: algebra, Sum
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 which the following expression can take : $$\frac{a^2}{b + c} + \frac{b^2}{c + a} + \frac{c^2}{a + b}.$$