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Résoudre \[\left\{\begin{aligned} a &+ &b &+ &c &= &0 \cr a^2 &+ &b^2 &+ &c^2 &= &1 \cr \frac 1a &+ &\frac 1b &+ &\frac 1c &= &-1.\cr\end{aligned}\right.\]
Résoudre \[\left\{\begin{aligned} a &+ &b &+ &c &= &0 \cr a^2 &+ &b^2 &+ &c^2 &= &1 \cr \frac 1a &+ &\frac 1b &+ &\frac 1c &= &-1.\cr\end{aligned}\right.\]