<s>[INST] Solve three equations with three unknowns Solve the system:
$$\begin{cases}a+b+c=6\\ab+ac+bc=11\\abc=6\end{cases}$$
The solution is:
$a=1,b=2,c=3$
How can I solve it?
 [/INST] As an alternative to the other derivations, here's my approach.
In the second equation, move everything to the left side, factor $ac+bc$ into $(a+b)c$, multiply everything by $c$, replace $a+b$ with $6-c $ from the first equation, and $abc$ with $6$ from the third. Then you have $6-11c+(6-c)c^2 = 0$, which simplifies to $c^3-6c^2+11c-6 = 0$, which has roots $1, 2,$ and $3$.
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