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МатематикаРешебник по алгебре 9 класс Макарычев Задание 534
Задание 534
\[\boxed{\text{534\ (534).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\left\{ \begin{matrix} 3x - 4y = - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x + y^{2} = 10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - y^{2} - x + y = 100 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} 3x = 4y - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4y - 2 + y^{2} = 10\ \ \ \ \ \ \ \ \ \\ x^{2} - y^{2} - x + y = 100 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y_{1} = - 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x = - 24 - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - y^{2} - x + y = 100 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y_{1} = - 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x_{1} = - \frac{26}{3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \left( \frac{26}{3} \right)^{2} - 36 + \frac{26}{3} - 6 \neq 100 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow корней\ нет.\]
\[или\ \ \left\{ \begin{matrix} y_{2} = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x = 8 - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - y^{2} - x + y = 100 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y_{2} = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x_{2} = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4 - 4 - 2 + 2 \neq 100 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow корней\ нет.\]
\[Ответ:система\ не\ имеет\ \]
\[решений.\]
\[\boxed{\text{534.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ a_{1} = 1;a_{n + 1} = a_{n} + 1\]
\[a_{2} = a_{1} + 1 = 2,\ \ \]
\[a_{3} = a_{2} + 1 = 3,\]
\[a_{4} = a_{3} + 1 = 4,\ \ \]
\[a_{5} = a_{4} + 1 = 5.\]
\[\textbf{б)}\ a_{1} = 1000;\ \ \ \ \ a_{n + 1} = 0,1a_{n}\text{\ \ }\]
\[a_{2} = 0,1 \cdot a_{1} = 100,\ \ \]
\[a_{3} = 0,1 \cdot a_{2} = 10,\]
\[a_{4} = 0,1 \cdot a_{3} = 1,\ \ \]
\[a_{5} = 0,1 \cdot a_{4} = 0,1.\]
\[\textbf{в)}\ a_{1} = 16;\ \ a_{n + 1} = - 0,5a_{n}\ \]
\[a_{2} = - 0,5 \cdot a_{1} = - 8,\ \ \]
\[a_{3} = - 0,5 \cdot a_{2} = 4,\]
\[a_{4} = - 0,5 \cdot a_{3} = - 2,\ \ \]
\[a_{5} = - 0,5 \cdot a_{4} = 1.\]
\[\textbf{г)}\ a_{1} = 3;\ \ a_{n + 1} = a_{n}^{- 1}\text{\ \ }\]
\[a_{2} = a_{1}^{- 1} = \frac{1}{3},\ \ \]
\[a_{3} = a_{2}^{- 1} = 3,\ \ \]
\[a_{4} = a_{3}^{- 1} = \frac{1}{3},\]
\[a_{5} = a_{4}^{- 1} = 3.\]
