\[\boxed{\text{788.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[\left\{ \begin{matrix} a \cdot b = 4\ \ \ \ \ \ \\ \sqrt{a} + \sqrt{b} = 3 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} a \cdot b = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ a + 2\sqrt{\text{ab}} + b = 9 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} ab = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \\ a + b + 4 = 9 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} ab = 4\ \ \ \ \ \ \\ a + b = 5 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\lbrack \begin{matrix} \left\{ \begin{matrix} a = 1 \\ b = 4 \\ \end{matrix} \right.\ \\ \left\{ \begin{matrix} a = 4 \\ b = 1 \\ \end{matrix} \right.\ \\ \end{matrix} \right.\ .\]