Найдите первый член и знаменатель геометрической прогрессии (bn), если: b10=9b8 и b3+b6=168.

\[b_{10} = 9b_{8};\ \ \ \ \ \ \ b_{3} + b_{6} = 168:\]

\[\left\{ \begin{matrix} b_{10} = 9b_{8}\text{\ \ \ \ \ \ \ \ } \\ b_{3} + b_{6} = 168 \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} b_{1}q^{9} = 9b_{1}q^{7}\ \ \ \ \ |:b_{1}q^{7} \\ b_{1}q^{2} + b_{1}q^{5} = 168\ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} q^{2} = 9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ b_{1}\left( q^{2} + q^{5} \right) = 168 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} q = 3 \\ b_{1} = \frac{2}{3} \\ \end{matrix}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} q = - 3\ \ \ \ \ \\ b_{1} = - \frac{28}{39} \\ \end{matrix} \right.\ \]

\[Ответ:\ \ q = 3,\ \ \ b_{1} = \frac{2}{3}\ \ или\ \ \ \]

\[q = - 3,\ \ \ \ b_{1} = - \frac{28}{39}.\]