Three, real numbers $a, b, c$ satisfy $\left\{\begin{array}{l}a^{2}-b c-6 a+3=0, \\ b^{2}+c^{2}+b c-2 a-1=0 .\end{array}\right.$ Find the range of values for $a$.
Three、 $\frac{10-2 \sqrt{19}}{3} \leqslant a \leqslant \frac{10+2 \sqrt{19}}{3}$.