Алгебра
Английский
Биология
География
Геометрия
История
Русский
Обществознание
Физика
Химия
Информатика
Литература
МатематикаРешебник по алгебре 9 класс Макарычев Задание 530
Задание 530
\[\boxed{\text{530}\text{\ (530)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \left\{ \begin{matrix} x^{2} + 3x - 4y = 20 \\ x^{2} - 2x + y = - 5\ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x^{2} - 3x - 4y = 20 \\ - x^{2} + 2x - y = 5\ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} 5x - 5y = 25 \\ 5x^{2} - 5x = 0\ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = 5 + y\ \ \ \ \ \\ x(x - 1) = 0 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x_{1} = 0 \\ y_{1} = 5 \\ \end{matrix} \right.\ \text{\ \ \ \ }\]
\[или\ \ \left\{ \begin{matrix} x_{2} = 1\ \ \ \ \\ y_{2} = - 4. \\ \end{matrix} \right.\ \]
\[\textbf{б)}\ \left\{ \begin{matrix} y^{2} + 3x - y = 1 \\ y^{2} + 6x - 2y = 1 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} 3x - y = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2y^{2} + 6x - 2y = 2\ \ \ \\ - y^{2} - 6x + 2y = - 1 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = 3x \\ y^{2} = 1\ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y_{1} = 1 \\ x_{1} = \frac{1}{3}\ \\ \end{matrix} \right.\ \ \ или\ \text{\ \ }\left\{ \begin{matrix} y_{2} = - 1\ \ \\ x_{2} = - \frac{1}{3}. \\ \end{matrix} \right.\ \]
\[Ответ:а)\ (0;5);(1;\ - 4);\ \ \]
\[\textbf{б)}\ \left( \frac{1}{3};1 \right);\left( - \frac{1}{3};\ - 1 \right).\]
\[\boxed{\text{530.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ x_{n} = 2n - 1\]
\[x_{1} = 2 - 1 = 1\]
\[x_{2} = 4 - 1 = 3\]
\[x_{3} = 6 - 1 = 5\]
\[x_{4} = 8 - 1 = 7\]
\[x_{5} = 10 - 1 = 9\]
\[x_{6} = 12 - 1 = 11;\]
\[\textbf{б)}\ x_{n} = n^{2} + 1\]
\[\ x_{1} = 1 + 1 = 2\]
\[x_{2} = 4 + 1 = 5\]
\[x_{3} = 9 + 1 = 10\]
\[x_{4} = 16 + 1 = 17\]
\[x_{5} = 25 + 1 = 26\]
\[x_{6} = 36 + 1 = 37\]
\[\textbf{в)}\ x_{n} = \frac{n}{n + 1}\]
\[x_{1} = \frac{1}{1 + 1} = \frac{1}{2}\]
\[x_{2} = \frac{2}{2 + 1} = \frac{2}{3}\]
\[x_{3} = \frac{3}{3 + 1} = \frac{3}{4}\]
\[x_{4} = \frac{4}{4 + 1} = \frac{4}{5}\]
\[x_{5} = \frac{5}{5 + 1} = \frac{5}{6}\]
\[x_{6} = \frac{6}{6 + 1} = \frac{6}{7}\ \]
\[\textbf{г)}\ x^{n} = ( - 1)^{n + 1} \cdot 2\ \]
\[x_{1} = ( - 1)^{2} \cdot 2 = 2\]
\[x_{2} = - 2\]
\[x_{3} = 2\]
\[x_{4} = - 2\]
\[x_{5} = 2\]
\[x_{6} = - 2;\]
\[\textbf{д)}\ x_{n} = 2^{n - 3}\ \]
\[x_{1} = 2^{- 2} = \frac{1}{4}\]
\[x_{2} = 2^{- 1} = \frac{1}{2}\]
\[x_{3} = 2^{0} = 1\]
\[x_{4} = 2^{1} = 2\]
\[x_{5} = 2^{2} = 4\]
\[x_{6} = 2³ = 8;\]
\[\textbf{е)}\ x^{n} = 0,5 \cdot 4^{n}\ \]
\[x_{1} = 0,5 \cdot 4 = 2\]
\[x_{2} = 0,5 \cdot 4^{2} = 8\]
\[x_{3} = 0,5 \cdot 4^{3} = 32\]
\[x_{4} = 0,5 \cdot 4^{4} = 128\]
\[x_{5} = 0,5 \cdot 4^{5} = 512\]
\[x_{6} = 0,5 \cdot 4^{6} = 2048.\]
