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МатематикаРешебник по алгебре 9 класс Мерзляк Задание 470
Задание 470
\[\boxed{\text{470\ (470).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\left\{ \begin{matrix} x^{2} + y^{2} = 9 \\ x - y = a\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ }\]
\[\left\{ \begin{matrix} x^{2} + (x - a)^{2} = 9 \\ y = x - a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\left\{ \begin{matrix} 2x^{2} - 2xa + a^{2} - 9 = 0 \\ y = x - a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[2x^{2} - 2xa + a^{2} - 9 = 0\]
\[D = 4a^{2} - 8a^{2} + 72 =\]
\[= - 4a^{2} + 72\]
\[1)\ Имеет\ одно\ решение\ \]
\[при\ D = 0:\]
\[- 4a^{2} + 72 = 0\]
\[a^{2} = 18\ \ \]
\[a = \pm \sqrt{18} = \pm 3\sqrt{2} -\]
\[одно\ решение.\]
\[2)\ Имеет\ два\ решения\ \]
\[при\ D > 0:\]
\[- 4a^{2} + 72 > 0\]
\[a^{2} > 18\]
\[a \in \left( - 3\sqrt{2};3\sqrt{2} \right) - два\ \]
\[решения.\]
\[3)\ Не\ имеет\ решений,\]
\[\ если\ D < 0:\]
\[- 4a^{2} + 72 < 0\ \ \]
\[a^{2} < 18\]
\[a \in \left( - \infty; - 3\sqrt{2} \right) \cup\]
\[\cup \left( 3\sqrt{2};\ + \infty \right) - нет\ решений.\]
\[Ответ:1)\ a = \pm 3\sqrt{2};\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ 2) - 3\sqrt{2} < a < 3\sqrt{2};\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ 3)\ a < - 3\sqrt{2}\ ,\ a > 3\sqrt{2}.\ \ \]
\[\boxed{\text{470.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ y = \frac{x^{3}}{|x|} + 4x\]
\[1.y = x^{2} + 4x,\ \ x > 0\]
\[y(1) = 1 + 4 = 5\]
\[x_{0} = - 2,\ \ y_{0} = - 4,\ \ \]
\[( - 2;\ - 4)\]
\[x = 0,\ \ y = 0,\ \ (0;0)\]
\[x(x + 4) = 0,\ \ x = 0,\]
\[\ \ x = - 4\ (не\ удовлетворяет),\]
\[\text{\ \ }(0;0)\]
\[2.\ y = - x^{2} + 4x,\ \ x < 0\]
\[y( - 1) = - 1 - 4 = - 5\]
\[x_{0} = 2,\ \ y_{0} = - 4 + 8 = 4,\ \ \]
\[(2;4)\]
\[x = 0,\ \ y = 0,\ \ (0;0)\]
\[- x(x - 4) = 0,\ \ x = 0,\]
\[\ \ x = 4\ (не\ удовлетворяет),\]
\[\text{\ \ }(0;0)\]
\[2)\ y = 6|x| - x^{2}\]
\[y = - x^{2} + 6x,\ \ x > 0\]
\[x_{0} = 3,\ \ y_{0} = 9,\ \ (3;9)\]
\[x = 0,\ \ y = 0,\ \ (0;0)\]
\[- x(x - 6) = 0\]
\[x = 0,\ \ (0;0)\]
\[x = 6,\ \ (6;0)\]
\[y( - 1) = - 1 + 6 = 5\]
\[y = - x^{2} - 6x,\ \ x < 0\]
\[x_{0} = - 3,\ \ y_{0} = 9,\ \ \]
\[( - 3;9)\]
\[x = 0,\ \ y = 0,\ \ \]
\[(0;0)\]
\[- x(x + 6) = 0\]
\[x = 0,\ \ (0;0)\]
\[x = - 6,\ \ ( - 6;0)\]
\[y( - 1) = - 1 + 6 = 5\]
