1
Étudier l’existence de solutions du système : \[\left\{\begin{array}{ccccccc} x &+& y &+& z &= &1 \cr ax &+& by &+& cz &= &d \cr a(a-1)x &+& b(b-1)y &+& c(c-1)z &= &d(d-1). \cr\end{array}\right.\]
Étudier l’existence de solutions du système : \[\left\{\begin{array}{ccccccc} x &+& y &+& z &= &1 \cr ax &+& by &+& cz &= &d \cr a(a-1)x &+& b(b-1)y &+& c(c-1)z &= &d(d-1). \cr\end{array}\right.\]