ГДЗ по алгебре 9 класс Макарычев Задание 378

\[\boxed{\text{378\ (378).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ y = \ \frac{1}{\sqrt{144 - 9x^{2}}}\text{\ \ }\]

\[144 - 9x^{2} > 0\]

\[9x^{2} - 144 < 0\]

\[9 \cdot \left( x^{2} - 14 \right) < 0\]

\[9 \cdot (x + 4)(x - 4) < 0\]

\[x \in ( - 4;4).\]

\[\textbf{б)}\ y = \frac{\sqrt{16 - 24x + 9x^{2}}}{x + 2}\]

\[\left\{ \begin{matrix} 9x^{2} - 24x + 16 \geq 0 \\ x + 2 \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} (3x - 4)^{2} \geq 0 \\ x \neq - 2\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow x \neq - 2.\]

\[x \in ( - \infty; - 2) \cup ( - 2; + \infty).\]