ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 1108

\[\boxed{\text{1108.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[\textbf{а)}\ y = \frac{x - \sqrt{x + 6}}{x + 5}\]

\[\left\{ \begin{matrix} x + 6 \geq 0 \\ x + 5 \neq 0 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x \geq - 6 \\ x \neq - 5 \\ \end{matrix} \right.\ \]

\[Область\ определения:\ \ \ \]

\[x \in \lbrack - 6;\ - 5) \cup ( - 5;\ + \infty);\]

\[x - \sqrt{x + 6} = 0\]

\[x = \sqrt{x + 6};\ \ x > 0\]

\[x^{2} = x + 6\]

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

\[x_{1} + x_{2} = 1;\ \ \ x_{1} \cdot x_{2} = - 6\]

\[x_{1} = 3;\ \ \ x_{2} =\]

\[= - 2\ (не\ подходит).\]

\[Ноль\ функции:\ \ \ \]

\[x = 3.\]

\[\textbf{б)}\ y = \frac{4x^{2} + 25x}{2x - \sqrt{10 - 6x}}\]

\[\left\{ \begin{matrix} 10 - 6x \geq 0\ \ \ \ \ \ \ \ \ \ \ \ \\ 2x - \sqrt{10 - 6x} \neq 0 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 6x \leq 10\ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x \neq \sqrt{10 - 6x} \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x \leq \frac{10}{6}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 4x^{2} \neq 10 - 6x \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x \leq \frac{5}{3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 2x² + 3x - 5 = 0 \\ \end{matrix} \right.\ \]

\[2x^{2} + 3x - 5 = 0\]

\[D = 9 + 4 \cdot 2 \cdot 5 = 49 = 7^{2}\]

\[x_{1} = \frac{- 3 + 7}{4} = \frac{1}{2};\ \ \ \]

\[x_{2} = \frac{- 3 - 7}{4} = - 2.\]

\[При\ x = - 2,5:\ \ \ \ \]

\[2x = - 5\]

\[\sqrt{10 - 6x} = 5.\]

\[Область\ определения:\ \ \]

\[\ x \in ( - \infty;1) \cup \left( 1;\frac{5}{3} \right\rbrack.\]

\[Нули\ функции:\]

\[4x^{2} + 25x = 0\]

\[x(4x + 25) = 0\]

\[x_{1} = 0;\]

\[4x_{2} = - 25\]

\[x_{2} = - 6\frac{1}{4}.\]