ГДЗ по алгебре 9 класс Макарычев Задание 352

\[\boxed{\text{352\ (352).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ x^{5} - x^{3} = 0\]

\[x^{3}\left( x^{2} - 1 \right) = 0\]

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

\[x_{1} = 0;\ \ x_{2} = 1;\ \ x_{3} = - 1.\]

\[Ответ:x = 0;x = \pm 1.\]

\[\textbf{б)}\ x^{6} = 4x^{4}\]

\[x^{6} - 4x^{4} = 0\]

\[x^{4} \cdot \left( x^{2} - 4 \right) = 0\]

\[x^{4} \cdot (x - 2)(x + 2) = 0\]

\[x_{1} = 0;\ \ x_{2} = 2;\ \ x_{3} = - 2.\]

\[Ответ:x = 0;\ \ x = \pm 2.\]

\[\textbf{в)}\ 0,5x^{3} = 32x\ \ \ \ | \cdot 2\]

\[x^{3} = 64x\]

\[x^{3} - 64x = 0\]

\[x\left( x^{2} - 64 \right) = 0\]

\[x(x - 8)(x + 8) = 0\]

\[x_{1} = 0;\ \ x_{2} = 8;\ \ x_{3} = - 8.\]

\[Ответ:x = 0;\ \ x = \pm 8.\]

\[\textbf{г)}\ 0,2x^{4} = 4x^{2}\ \ \ \ \ \ \ \ | \cdot 5\]

\[x^{4} = 20x^{2}\]

\[x^{4} - 20x^{2} = 0\]

\[x^{2}\left( x^{2} - 20 \right) = 0\]

\[x^{2}\left( x - \sqrt{20} \right)\left( x + \sqrt{20} \right) = 0\]

\[x_{1} = 0;\ \ x_{2} = \sqrt{20} = 2\sqrt{5};\ \]

\[\ x_{3} = - 2\sqrt{5}.\]

\[Ответ:x = 0;\ \ x = \pm 2\sqrt{5}.\]