\[\boxed{\text{502.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\left( ax^{2} - 2x + b \right)\left( x^{2} + ax - 1 \right) =\]
\(По\ условию\ коэффициенты\ \)
\[при\ x^{2}\ и\ \text{x\ }\ равны\ 8\ и\ ( - 2):\]
\[\left\{ \begin{matrix} b - 3a = 8\ \ \\ 2 + ab = - 2 \\ \end{matrix} \Longrightarrow \right.\ \]
\[\Longrightarrow \left\{ \begin{matrix} b = 3a + 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ a(3a + 8) + 4 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} b = 3a + 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3a² + 8a + 4 = 0 \\ \end{matrix} \right.\ \ \]
\[3a^{2} + 8a + 4 = 0\]
\[D = 16 - 12 = 4\]
\[a_{1,2} = \frac{- 4 \pm 2}{3};\]
\[\left\{ \begin{matrix} a_{1} = - 2 \\ b_{1} = 2\ \ \ \\ \end{matrix} \right.\ \ \ или\ \ \ \left\{ \begin{matrix} a_{2} = - \frac{2}{3} \\ b_{2} = 6\ \ \ \ . \\ \end{matrix} \right.\ \]
\[Ответ:a = - 2,\ b = 2\ \ или\ \]
\[\ a = - \frac{2}{3},b = 6.\]