An algebra problem by Rajdeep Ghosh

Algebra Level 3

Suppose that \( a, b, c \) are non-zero complex numbers that satisfy

\[ a^2 = b + c \\ b^2 = c + a \\ c^2 = a + b \]

Find the value of \[\frac{a}{a+1}+\frac{b}{b+1}+\frac{c}{c+1} .\]

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