11. Solve the system of equations:

$$
\left\{\begin{array}{l}
a^{2}+3 a+1=(b+c) / 2 \\
b^{2}+3 b+1=(a+c) / 2 \\
c^{2}+3 c+1=(a+b) / 2
\end{array}\right.
$$
92.11. Adding all the equations, we get $(a+1)^{2}+(b+1)^{2}+$ $+(c+1)^{2}=0$. From this, $a=b=c=-1$. This is the only solution to the system.