Решебник по алгебре 9 класс Макарычев Задание 531

 

\[\boxed{\text{531}\text{\ (531)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \left\{ \begin{matrix} x + y + xy = 5\ \ \\ xy + x - y = 13 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 2y = - 8\ \ \ \ \ \ \ \ \ \ \ \ \\ x + y + xy = 5 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} y = - 4\ \ \ \ \ \ \ \ \ \ \ \ \ \\ x - 4 - 4x = 5 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow y = - 4,\ \ x = - 3.\]

\[Ответ:( - 3;\ - 4).\]

\[\textbf{б)}\ \left\{ \begin{matrix} x + xy + y = 10\ \\ xy - 2x - 2y = 2 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 2x + 2xy + 2y = 20 \\ xy - 2x - 2y = 2\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} 3xy = 22\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ xy - 2x - 2y = 2 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = \frac{22}{3y}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \frac{22}{3y} - \frac{44}{3y} - 2y - 2 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = \frac{22}{3y}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 11y - 22 - 3y^{2} - 3y = 0 \\ \end{matrix} \right.\ \]

\[3y^{2} - 8y + 22 = 0\]

\[D = 16 - 3 \cdot 22 < 0 \Longrightarrow корней\ \]

\[нет.\]

\[Ответ:корней\ нет.\]

\[\boxed{\text{531.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[b_{n} = 2n^{2} + 3n\]

\[\textbf{а)}\ b_{5} = 2 \cdot 5² + 3 \cdot 5 =\]

\[= 50 + 15 = 65;\]

\[\textbf{б)}\ b_{10} = 2 \cdot 10² + 3 \cdot 10 =\]

\[= 200 + 30 = 230;\]

\[\textbf{в)}\ b_{50} = 2 \cdot 50² + 3 \cdot 50 = 5150.\]