\[x^{2} - 2ax + a^{2} - 1 = 0\]
\[x^{2} - 2ax + \left( a^{2} - 1 \right) = 0\]
\[D = 4a^{2} - 4 \cdot \left( a^{2} - 1 \right) =\]
\[= 4a^{2} - 4a^{2} + 4 = 4\]
\[x_{1} = \frac{2a + 2}{2} = a + 1;\ \ \]
\[x_{2} = \frac{2a - 2}{2} = a - 1.\]
\[\left\{ \begin{matrix} 1 < a + 1 < 5 \\ 1 < a - 1 < 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} 0 < a < 4 \\ 2 < a < 6 \\ \end{matrix} \right.\ \]
\[a \in (2;4).\]
\[Ответ:при\ a \in (2;4).\]