Решебник по алгебре 9 класс Мерзляк Задание 437

 

\[\boxed{\text{437\ (437).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \left\{ \begin{matrix} x^{2} - 5x + 4 > 0 \\ x > a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[x^{2} - 5x + 4 > 0\]

\(x_{1} + x_{2} = 5,\ \ \ \ \ \ \ \ \ \ \ x_{1} = 4\)

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

\[Если\ a < 1;\ \ то\ a < x < 1\ \ \]

\[\ или\ \ x > 4.\]

\[Если\ 1 \leq a \leq 4;\ \ то\ x > 4.\]

\[Если\ a > 4;\ \ то\ x > a\text{.\ }\]

\[2)\ \left\{ \begin{matrix} 4x^{2} - 3x - 1 \leq 0 \\ x < a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[4x^{2} - 3x - 1 \leq 0\]

\[D = 9 + 16 = 25\]

\[x_{1} = \frac{3 + 5}{8} = 1\]

\[x_{2} = \frac{3 - 5}{8} = - \frac{1}{4} = - 0,25\]

\[Если\ a \leq - 0,25;\ \ то\ нет\ \]

\[решений.\]

\[Если - 0,25 < a \leq 1;\ \ \]

\[то\ - 0,25 \leq x < a.\]

\[Если\ a > 1;\ \ то\ - 0,25 \leq x \leq 1.\]

\[\boxed{\text{437.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[y = x^{2} + 4x + 1\]

\[x_{0} = - \frac{4}{2} = - 2;\]

\[y_{0} = 4 - 8 + 1 = - 3.\]

\[Oy:\ \ x = 0,\ \ y = 1.\]

\[y(1) = 1 + 4 + 1 = 6.\]

\[y = \frac{6}{x}\]

\[Ответ:3\ корня.\]