Решебник по алгебре 9 класс Макарычев Задание 953

 

\[\boxed{\text{953\ (953).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ x^{4} - 16x^{2} = 0\]

\[x^{2}\left( x^{2} - 16 \right) = 0\]

\[x^{2} = 0,\ \ x = 0;\]

\[x^{2} - 16 = 0\]

\[x^{2} = 16\]

\[x = \pm 4.\]

\[Ответ:x = 0;x = 4;\ x = - 4.\]

\[\textbf{б)}\ x = x³\]

\[x - x^{3} = 0\]

\[x\left( 1 - x^{2} \right) = 0\]

\[x = 0,\]

\[1 - x^{2} = 0\]

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

\[Ответ:x = 0;x = 1;\ x = - 1.\]

\[\textbf{в)}\ 1,2x³ + x = 0\]

\[x\left( 1,2x^{2} + 1 \right) = 0\]

\[x = 0,\]

\[1,2x^{2} + 1 = 0\]

\[1,2x² = - 1 \Longrightarrow нет\ корней.\]

\[Ответ:x = 0.\]

\[\textbf{г)}\ 0,4x^{4} = x³\]

\[0,4x^{4} - x^{3} = 0\]

\[x^{3}(0,4x - 1) = 0\]

\[x^{3} = 0,\ \ x = 0,\]

\[0,4x - 1 = 0\]

\[0,4x = 1\]

\[x = 2,5.\]

\[Ответ:x = 0;x = 2,5.\]

\[\textbf{д)}\ x³ + 6x² - 16x = 0\]

\[x\left( x^{2} + 6x - 16 \right) = 0\]

\[x^{2} + 6x - 16 = 0\]

\[D = 36 + 64 = 100\]

\[x_{1} = \frac{- 6 + 10}{2} = 2,\]

\[x_{2} = \frac{- 6 - 10}{2} = - 8,\ \ x_{3} = 0.\]

\[Ответ:x = 0;x = 2;\ x = - 8.\]

\[\textbf{е)}\ x^{4} + x³ - 6x^{2} = 0\]

\[x^{2}\left( x^{2} + x - 6 \right) = 0\]

\[x² + x - 6 = 0\]

\[D = 1 + 24 = 25\]

\[x_{1} = \frac{- 1 + 5}{2} = 2,\]

\[x_{2} = \frac{- 1 - 5}{2} = - 3,\ \ x_{3} = 0.\]

\[Ответ:x = 0;x = 2;\ x = - 3.\]

\[\textbf{ж)}\ x³ + x² = 9x + 9\]

\[x^{2}(x + 1) = 9(x + 1)\]

\[(x + 1)\left( x^{2} - 9 \right) = 0\]

\[x + 1 = 0,\ \ x = - 1,\]

\[x^{2} - 9 = 0,\ \ x^{2} = 9,\]

\[x = \pm 3.\]

\[Ответ:\ x = - 1;\ x = - 3;x = 3.\]

\[\textbf{з)}\ 2x³ + 8x = x² + 4\ \]

\[2x\left( x^{2} + 4 \right) = x^{2} + 4\]

\[(x² + 4)(2x - 1) = 0\]

\[x^{2} + 4 = 0,\ \ \]

\[x^{2} = - 4 \Longrightarrow корней\ нет.\]

\[2x - 1 = 0,\ \ 2x = 1,\]

\[x = 0,5.\]

\[Ответ:x = 0,5.\]