\[\boxed{\text{537\ (537).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\left( ax^{2} - 2x + b \right)\left( x^{2} + ax - 1 \right) =\]
\[По\ условию\ коэффициенты\ при\ \]
\[x^{2}\ и\ \text{x\ }\ равны\ 8\ и\ ( - 2):\]
\[\left\{ \begin{matrix} b - 3a = 8\ \ \\ 2 + ab = - 2 \\ \end{matrix} \Longrightarrow \right.\ \]
\[\Longrightarrow \left\{ \begin{matrix} b = 3a + 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ a(3a + 8) + 4 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} b = 3a + 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3a² + 8a + 4 = 0 \\ \end{matrix} \right.\ \ \]
\[3a^{2} + 8a + 4 = 0\]
\[D = 16 - 12 = 4\]
\[a_{1,2} = \frac{- 4 \pm 2}{3};\]
\[\left\{ \begin{matrix} a_{1} = - 2 \\ b_{1} = 2\ \ \ \\ \end{matrix} \right.\ \ \ или\ \ \ \left\{ \begin{matrix} a_{2} = - \frac{2}{3} \\ b_{2} = 6\ \ \ \ . \\ \end{matrix} \right.\ \]
\[Ответ:a = - 2,\ b = 2\ \ или\]
\[a = - \frac{2}{3},b = 6.\]
\[\boxed{\text{537.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ 4x^{4} + 4x² - 15 = 0\]
\[Пусть\ t = x^{2},\ t \geq 0,\ тогда:\]
\[4t^{2} + 4t - 15 = 0\]
\[D = 4 + 4 \cdot 15 = 64\]
\[t_{1,2} = \frac{- 2 \pm 8}{4},\ \ так\ как\]
\[\ t \geq 0,\ то\ t = 1,5.\]
\[\Longrightarrow x^{2} = 1,5 \Longrightarrow x = \pm \sqrt{1,5}.\]
\[Ответ:x = \pm \sqrt{1,5}.\]
\[\textbf{б)}\ 2x^{4} - x^{2} - 36 = 0\]
\[Пусть\ t = x^{2},\ t \geq 0,\ тогда:\]
\[2t^{2} - t - 36 = 0\]
\[D = 1 + 4 \cdot 2 \cdot 36 = 289\]
\[t_{1,2} = \frac{1 \pm 17}{4},\ \ так\ как\ \]
\[t \geq 0,\ то\ \ t = 4,5;\]
\[x² = 4,5 \Longrightarrow x = \pm \sqrt{4,5}.\]
\[Ответ:x = \pm \sqrt{4,5}.\]