Решебник по алгебре 9 класс Мерзляк Задание 438

 

\[\boxed{\text{438\ (438).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\left\{ \begin{matrix} x^{2} - x - 72 < 0 \\ x > a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[x^{2} - x - 72 < 0\]

\(x_{1} + x_{2} = 1,\ \ \ \ \ \ \ \ \ \ \ x_{1} = 9\)

\[x_{1}x_{2} = - 72,\ \ x_{2} = - 8\]

\[Если\ a < - 8,\]

\[\ \ то - 8 < x < 9.\]

\[Если - 8 < a < 9,\]

\[\text{\ \ }то\ a < x < 9.\]

\[Если\ a \geq 9,\ \ \]

\[то\ нет\ решений.\]

\[2)\ \left\{ \begin{matrix} x^{2} - 9x + 8 > 0 \\ x < a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[x^{2} - 9x + 8 > 0\]

\(x_{1} + x_{2} = 9,\ \ \ \ \ \ \ \ \ \ \ x_{1} = 8\)

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

\[Если\ a < 1,\ \ то\ x < a.\]

\[Если\ 1 < a < 8,\ \ то\ x < 1.\]

\[Если\ a > 8,\ \ \]

\[то\ x < 1\ \ и\ \ 8 < x < a\text{.\ }\]

\[\boxed{\text{438.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[y = - x^{2} + 9x + 9\]

\[1)\ x = y\]

\[- x^{2} + 9x + 9 = x\]

\[x^{2} - 8x - 9 = 0\]

\[x_{1} + x_{2} = 8,\ \ x_{1}x_{2} = - 9\]

\[x_{1} = 9,\ \ x_{2} = - 1.\]

\[Ответ:(9;9),\ \ \ ( - 1; - 1).\]

\[2)\ x + y = 25,\ \ y = 25 - x\]

\[- x^{2} + 9x + 9 = 25 - x\]

\[x^{2} - 10x + 16 = 0\]

\[x_{1} + x_{2} = 10,\ \ x_{1} = 8\]

\[x_{1}x_{2} = 16,\ \ x_{2} = 2.\]

\[x = 8,\ \ y = 17;\]

\[x = 2,\ \ y = 23.\]

\[Ответ:(8;17),\ \ \ (2;23).\]