ГДЗ по алгебре 9 класс Макарычев ФГОС Задание 282

\[\boxed{\text{283.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ y^{4} - 24y^{2} - 25 = 0\]

\[Пусть\ t = y^{2},\ \ t^{2} = y^{4},\]

\[\ \ t > 0;\]

\[t^{2} - 24t - 25 = 0\]

\[D = 144 + 25 = 169\]

\[t_{1,2} = 12 \pm 13 = 25; - 1.\]

\[Так\ как\ t > 0,\ то\ t = 25 \Longrightarrow\]

\[\Longrightarrow y^{2} = 25 \Longrightarrow y = \pm 5.\]

\[Ответ:y = \pm 5.\]

\[\textbf{б)}\ x^{4} - 9x^{2} + 18 = 0\]

\[Пусть\ t = x^{2},\ t^{2} = x^{4},\ t > 0;\]

\[t^{2} - 9t + 18 = 0\]

\[D = 81 - 4 \cdot 18 = 9\]

\[t_{1,2} = \frac{9 \pm 3}{2} = 3;6;\]

\[\left\{ \begin{matrix} x² = 3 \\ x² = 6 \\ \end{matrix} \Longrightarrow \right.\ \left\{ \begin{matrix} x_{1,2} = \pm \sqrt{3} \\ x_{3,4} = \pm \sqrt{6}. \\ \end{matrix} \right.\ \]

\(Ответ:x = \pm \sqrt{3};\ \ x = \pm \sqrt{6}.\)