ГДЗ по алгебре 9 класс Макарычев ФГОС Задание 333

\[\boxed{\text{334.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ \frac{x^{4}\ }{x^{2} - 2} + \frac{1 - 4x^{2}}{2 - x^{2}} + 4 = 0\]

\[\frac{x^{4}}{x^{2} - 2} - \frac{1 - 4x^{2}}{x^{2} - 2} + 4 = 0\]

\[\frac{x^{4} - 1 + 4x^{2} + 4x^{2} - 8}{x^{2} - 2} = 0\]

\[ОДЗ:x^{2} - 2 \neq 0,\ \ x^{2} \neq 2,\]

\[\ \ x \neq \pm \sqrt{2}.\]

\[x^{4} + 8x^{2} - 9 = 0;\]

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

\[\ \ y \geq 0.\]

\[y^{2} + 8y - 9 = 0,\ \ по\ теореме\ \]

\[Виета:\]

\[y_{1} = 1,\ \ y_{2} = - 9.\]

\[Так\ как\ y \geq 0,\ \ то\ y = 1;\]

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

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

\[\ \ y \geq 0,\]

\[\frac{y + 3}{y + 1} + \frac{2}{y - 4} + \frac{10}{y^{2} - 3y - 4} = 0\]

\[\frac{y + 3}{y + 1} + \frac{2}{y - 4} + \frac{10}{(y - 4)(y + 4)} = 0\]

\[\frac{(y + 3)(y - 4) + 2 \cdot (y + 1) + 10}{(y - 4)(y + 1)} = 0\]

\[ОДЗ:\ \ \ y \neq 4;\ - 1;\]

\[y^{2} - 4y + 3y - 12 + 2y + 2 + 10 = 0\]

\[y^{2} + y = 0\]

\[y(y + 1) = 0\]

\[y_{1} = 0,\ \ y_{2} = - 1.\]

\[Так\ как\ y \geq 0 \Longrightarrow y = 0 \Longrightarrow\]

\[\Longrightarrow x^{2} = 0 \Longrightarrow x = 0.\]

\[Ответ:\ \ а) - 1;1;\ \ \ б)\ 0.\]