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МатематикаГДЗ по алгебре 9 класс Макарычев Задание 449
Задание 449
\[\boxed{\text{449\ (}\text{н}\text{).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \left\{ \begin{matrix} x^{2} + y^{2} = 36 \\ y = x^{2} + 6\ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x^{2} + y^{2} = 36 \\ x^{2} = y - 6\ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y^{2} + y - 42 = 0 \\ x^{2} = y - 6\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[y^{2} + y - 42 = 0\]
\[y_{1} + y_{2} = - 1;\ \ \ y_{1} \cdot y_{2} = - 42\]
\[y_{1} = 6;\ \ \ y_{2} = - 7.\]
\[\Longrightarrow \left\{ \begin{matrix} y = 6 \\ x = 0 \\ \end{matrix} \right.\ \text{\ \ \ }или\ \ \ \ \]
\[\left\{ \begin{matrix} y = - 7\ \ \ \ \\ x^{2} = - 13 \\ \end{matrix} \right.\ \Longrightarrow корней\ нет.\]
\[\textbf{б)}\ \left\{ \begin{matrix} x^{2} + y^{2} = 16\ \ \ \ \ \ \ \ \ \ \\ (x - 2)^{2} + y^{2} = 36 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y^{2} = 16 - x^{2}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ (x - 2)^{2} + 16 - x^{2} = 36 \\ \end{matrix} \right.\ \]
\[(x - 2)^{2} + 16 - x^{2} = 36\]
\[x^{2} - 4x + 4 + 16 - x^{2} = 36\]
\[- 4x = 36 - 20\]
\[- 4x = 16\]
\[x = - 4.\]
\[\left\{ \begin{matrix} y^{2} = 16 - 4^{2} \\ x = - 4\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y^{2} = 0 \\ x = - 4 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 0 \\ x = - 4 \\ \end{matrix}. \right.\ \]
\[\textbf{в)}\ \left\{ \begin{matrix} x^{2} + y^{2} = 25 \\ 4x - y = 0\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} y^{2} = 25 - x^{2} \\ y = 4x\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} y = 4x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (4x)^{2} = 25 - x^{2} \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = 4x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 16x^{2} + x^{2} = 25 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} y = 4x\ \ \ \ \ \ \\ 17x^{2} = 25 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} x = \pm \sqrt{\frac{25}{17}} \\ y = 4x\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = \pm 1,25 \\ y = \pm 5\ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:а)\ (0;6);\ \ б)\ ( - 4;0);\ \ \]
\[\textbf{в)}\ ( - 1,25; - 5);(1,25;5)\text{.\ }\]
\[\boxed{\text{449\ (}\text{с}\text{).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \left\{ \begin{matrix} x^{2} + y^{2} = 36 \\ y = x^{2} + 6\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x^{2} + y^{2} = 36 \\ x^{2} = y - 6\ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y^{2} + y - 42 = 0 \\ x^{2} = y - 6\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[y^{2} + y - 42 = 0\]
\[y_{1} + y_{2} = - 1;\ \ \ \]
\[y_{1} \cdot y_{2} = - 42\]
\[y_{1} = 6;\ \ \ y_{2} = - 7.\]
\[\Longrightarrow \left\{ \begin{matrix} y = 6 \\ x = 0 \\ \end{matrix} \right.\ \text{\ \ \ }или\ \ \ \ \]
\[\left\{ \begin{matrix} y = - 7\ \ \ \ \\ x^{2} = - 13 \\ \end{matrix} \right.\ \Longrightarrow корней\ нет.\]
\[\textbf{б)}\ \left\{ \begin{matrix} x^{2} + y^{2} = 16\ \ \ \ \ \ \ \ \ \ \\ (x - 2)^{2} + y^{2} = 36 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y^{2} = 16 - x^{2}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ (x - 2)^{2} + 16 - x^{2} = 36 \\ \end{matrix} \right.\ \]
\[(x - 2)^{2} + 16 - x^{2} = 36\]
\[x^{2} - 4x + 4 + 16 - x^{2} = 36\]
\[- 4x = 36 - 20\]
\[- 4x = 16\]
\[x = - 4.\]
\[\left\{ \begin{matrix} y^{2} = 16 - 4^{2} \\ x = - 4\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} y^{2} = 0 \\ x = - 4 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 0\ \ \ \\ x = - 4 \\ \end{matrix}. \right.\ \]
\[Ответ:а)\ (0;6);\ \ б)\ ( - 4;0).\]
