An algebra problem by Jose RL

Algebra Level 3

Let \( a,b\) and \(c\) real numbers such that

\[ \frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} = 1.\]

Find the value of

\[ \frac{a^2 }{b+c} + \frac{b^2}{c+a} + \frac{c^2}{a+b} . \]

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