3. Given real numbers $a, b, c$ satisfy
$$
a^{2}-b c-6 a+1=0, b^{2}+c^{2}+b c-2 a-1=0 \text {. }
$$

Find the range of values for $a$.
Answer: $\frac{10-\sqrt{94}}{3} \leqslant a \leqslant \frac{10+\sqrt{94}}{3}$.