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МатематикаРешебник по алгебре 9 класс Макарычев Задание 335
Задание 335
\[\boxed{\text{335\ (335).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \frac{x - 21}{x + 7} < 0\]
\[(x - 21)(x + 7) < 0\]
\[x \in ( - 7;21);\]
\[\textbf{б)}\ \frac{x + 4,7}{x - 7,2} > 0\]
\[(x + 4,7)(x - 7,2) > 0\]
\[x \in ( - \infty;\ - 4,7) \cup (7,2; + \infty).\]
\[\textbf{в)}\ \frac{6x + 1}{3 + x} > 0\]
\[(6x + 1)(x + 3) > 0\]
\[6 \cdot (x + 3)\left( x + \frac{1}{6} \right) > 0\]
\[x \in ( - \infty;\ - 3) \cup \left( - \frac{1}{6}; + \infty \right).\]
\[\textbf{г)}\ \frac{5x}{4x - 12} < 0\]
\[5x(4x - 12) < 0\]
\[20x(x - 3) < 0\]
\[x \in (0;3).\]
\[\boxed{\text{335.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ \left( \frac{x + 1}{x - 2} \right)^{2} - 16 \cdot \left( \frac{x - 2}{x + 1} \right)^{2} =\]
\[= 15\]
\[Пусть\ \ t = \left( \frac{x + 1}{x - 2} \right)^{2}:\]
\[\ t - \frac{16}{t} = 15\]
\[t^{2} - 15t - 16 = 0\]
\[По\ теореме\ Виета:\]
\[t_{1} + t_{2} = 15;\ \ \ t_{1} \cdot t_{2} = - 16\]
\[t_{1} = 16;\ \ \ \ t_{2} = - 1.\]
\[\left( \frac{x + 1}{x - 2} \right)^{2} = 16\ \ \]
\[\frac{x + 1}{x - 2} = \pm 4\]
\[1)\ \ \ \]
\[\frac{x + 1}{x - 2} = 4\ \]
\[x + 1 = 4x - 8\]
\[3x = 9\ \ \]
\[x = 3.\]
\[2)\ \frac{x + 1}{x - 2} = - 4\]
\[x + 1 = - 4x - 8\]
\[5x = 7\]
\[x = 1,4.\]
\[\left( \frac{x + 1}{x - 2} \right)^{2} = - 1 \Longrightarrow корней\ нет.\]
\[Ответ:x = 1,4;\ \ x = 3.\]
\[\textbf{б)}\ \left( \frac{x + 3}{x - 5} \right)^{2} - 9 \cdot \left( \frac{x - 5}{x + 3} \right)^{2} = 8;\]
\[Пусть\ t = \left( \frac{x + 3}{x - 5} \right)^{2}:\ \]
\[t - \frac{9}{t} = 8\]
\[t^{2} - 8t - 9 = 0\ \ \]
\[D_{1} = 16 + 9 = 25\]
\[t_{1} = 4 + 5 = 9;\ \ \]
\[\ t_{2} = 4 - 5 = - 1.\]
\[\left( \frac{x + 3}{x - 5} \right)^{2} = 9\ \ \]
\[\frac{x + 3}{x - 5} = \pm 3.\]
\[1)\ \frac{x + 3}{x - 5} = 3\text{\ \ }\]
\[x + 3 = 3x - 15\]
\[2x = 18\]
\[x = 9.\]
\[2)\ \frac{x + 3}{x - 5} = - 3\ \]
\[x + 3 = - 3x + 15\]
\[4x = 12\]
\[x = 3.\]
\[2)\ \ \left( \frac{x + 3}{x - 5} \right)^{2} = - 1 \Longrightarrow\]
\[\Longrightarrow корней\ нет.\]
\[Ответ:x = 3;x = 9.\]
