ГДЗ по алгебре 9 класс Макарычев Задание 219

\[\boxed{\text{219}\text{\ (219)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\left\{ \begin{matrix} \alpha \cdot \beta = 4\ \ \ \ \ \ \ \ \ \\ \sqrt{\alpha} + \sqrt{\beta} = 3 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} \alpha \cdot \beta = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \left( \sqrt{\alpha} + \sqrt{\beta} \right)^{2} = 3^{2} \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} \alpha \cdot \beta = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \alpha + 2\sqrt{\text{αβ}} + \beta = 9 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\left\{ \begin{matrix} \alpha\beta = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \alpha + 2 \cdot 2 + \beta = 9 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} \alpha\beta = 4\ \ \ \ \ \ \\ \alpha + \beta = 5 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\lbrack \begin{matrix} \left\{ \begin{matrix} \alpha = 1 \\ \beta = 4 \\ \end{matrix} \right.\ \\ \left\{ \begin{matrix} \alpha = 4 \\ \beta = 1 \\ \end{matrix} \right.\ \\ \end{matrix} \right.\ .\]