Решебник по алгебре 9 класс Мерзляк Задание 219

\[\boxed{\text{219\ (219).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \frac{x^{2}}{x^{2} - 16} = \frac{3x + 4}{x^{2} - 16}\text{\ \ \ }| \cdot \left( x^{2} - 16 \right)\]

\[\left\{ \begin{matrix} x^{2} = 3x + 4 \\ x^{2} - 16 \neq 0 \\ \end{matrix} \right.\ \]

\[x^{2} - 3x - 4 = 0\]

\[x_{1} + x_{2} = 3,\ \ x_{1} = 4\]

\[x_{1}x_{2} = - 4,\ \ \ \ \ \ \ \ \ \ \ x_{2} = - 1\]

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

\[x^{2} \neq 16\]

\[x \neq 4\]

\[x \neq - 4\]

\[Ответ:\ x = - 1.\]

\[2)\ \frac{5^{\backslash x}}{x - 3} - \frac{8^{\backslash x - 3}}{x} = 3\]

\[\frac{5x - 8x + 24}{x(x - 3)} = 3\ \ \ \ \ | \cdot x(x - 3)\]

\[\left\{ \begin{matrix} - 3x + 24 = 3x \cdot (x - 3) \\ x \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} - 3x + 24 = 3x^{2} - 9x \\ x \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[- 3x^{2} + 6x + 24 = 0\ \ \ \ |\ :( - 3)\]

\[x^{2} - 2x - 8 = 0\]

\[x_{1} + x_{2} = 2,\ \ x_{1} = 4\]

\[x_{1}x_{2} = - 8,\ \ \ \ \ \ \ \ \ \ \ x_{2} = - 2\]

\[Ответ:\ x = - 2;x = 4.\ \ \]