Решебник по алгебре 9 класс Макарычев Задание 951

 

\[\boxed{\text{951\ (951).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ 4x^{4} - 17x^{2} + 4 = 0\]

\[Пусть\ x^{2} = t,\ \ t \geq 0,\]

\[4t^{2} - 17t + 4 = 0\]

\[D = 289 - 64 = 225\]

\[t_{1} = \frac{17 + 15}{8} = 4,\]

\[t_{2} = \frac{17 - 15}{8} = \frac{2}{8} = \frac{1}{4},\]

\[1)\ x² = 4\]

\[x_{1,2} = \pm 2;\]

\[2)\ x² = \frac{1}{4},\]

\[x_{3,4} = \pm \frac{1}{2}.\]

\[Ответ:x = \pm 2;\ \ x = \pm \frac{1}{2}.\]

\[\textbf{б)}\ 9x^{4} + 77x² - 36 = 0\]

\[Пусть\ x^{2} = t,\ \ t \geq 0,\]

\[9t^{2} + 77t - 36 = 0\]

\[D = 5929 + 1296 = 7225\]

\[t_{1} = \frac{- 77 - 85}{18} = - 9 \Longrightarrow не\ \]

\[подходит.\text{\ \ }\]

\[t_{2} = \frac{- 77 + 85}{18} = \frac{4}{9},\]

\[x² = \frac{4}{9},\ \ x_{1,2} = \pm \frac{2}{3}.\]

\[Ответ:x = \pm \frac{2}{3}.\]

\[\textbf{в)}\ 2x^{4} - 9x^{2} - 5 = 0\]

\[Пусть\ x^{2} = t,\ \ t \geq 0,\]

\[2t^{2} - 9t - 5 = 0\]

\[D = 81 + 40 = 121,\]

\[t_{1} = \frac{9 - 11}{4} = - \frac{1}{2} \Longrightarrow не\ \]

\[подходит.\]

\[t_{2} = \frac{9 + 11}{4} = 5,\]

\[x² = 5,\ \ x = \pm \sqrt{5}.\]

\[Ответ:x = \pm \sqrt{5}.\]

\[\textbf{г)}\ 6x^{4} - 5x^{2} - 1 = 0\]

\[Пусть\ x^{2} = t,\ \ t \geq 0,\]

\[6t^{2} - 5t - 1 = 0\]

\[D = 25 + 24 = 49\]

\[t_{1} = \frac{5 + 7}{12} = 1,\]

\[t_{2} = \frac{5 - 7}{12} = - \frac{1}{6} \Longrightarrow не\ \]

\[подходит.\]

\[x^{2} = 1,\ \ x = \pm 1.\]

\[Ответ:x = \pm 1.\]