Решебник по алгебре 9 класс Мерзляк Задание 428

\[\boxed{\text{428\ (428).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ y = \sqrt{20 + 4x - 3x^{2}} +\]

\[+ \frac{3}{\sqrt{8 - 4x}}\]

\[\left\{ \begin{matrix} 20 + 4x - 3x^{2} \geq 0 \\ 8 - 4x > 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[1)\ - 3x^{2} + 4x + 20 \geq 0\]

\[D = 16 + 240 = 256\]

\[x_{1,2} = \frac{- 4 \pm 16}{- 6}\]

\[x = - 2;\ \ \ x = 3\]

\[2)\ 8 - 4x > 0\]

\[8 > 4x\]

\[x < 2\]

\[\left\{ \begin{matrix} (x + 2)(x - 3) \geq 0 \\ x < 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:x \in \lbrack - 2;2).\]

\[2)\ y = \frac{x + 5}{\sqrt{35 + 2x - x^{2}}} + \frac{x - 1}{|x| - 6}\]

\[\left\{ \begin{matrix} 35 + 2x - x^{2} > 0 \\ |x| - 6 \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[1)\ - x^{2} + 2x + 35 > 0\]

\(x_{1} + x_{2} = 2,\ \ \ \ \ \ \ \ \ \ \ x_{1} = 7\)

\[x_{1}x_{2} = - 35,\ \ x_{2} = - 5\]

\[2)\ |x| - 6 \neq 0\]

\[x \neq 6\]

\[x \neq - 6\]

\[\left\{ \begin{matrix} (x - 7)(x + 5) > 0 \\ x \neq 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq - 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:x \in ( - 5;6) \cup (6;7).\]