\[\boxed{\text{781.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[x^{2} + px + q = 0\]
\[\textbf{а)}\ \left\{ \begin{matrix} 3x_{1} + 3x_{2} = - 3p \\ 3x_{1} \cdot 3x_{2} = 9q\ \ \ \ \ \\ \end{matrix} \right.\ \ \ \ \ \ \Longrightarrow\]
\[\Longrightarrow \ x^{2} + 3p + 9q = 0\]
\[\textbf{б)}\ \left\{ \begin{matrix} x_{1} + 2 + x_{2} + 2 = - p \\ \left( x_{1} + 2 \right)\left( x_{2} + 2 \right) = q \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]
\[\text{\ \ }\left\{ \begin{matrix} x_{1} + x_{2} = - p - 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x_{1}x_{2} + 2x_{1} + 2x_{2} + 4 = q \\ \end{matrix} \right.\ \]
\[Получим\ уравнение:\ \ \ x^{2} +\]
\[+ (p + 4)x + q - 4 + 2 \cdot (p + 4)\text{.\ }\]