ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 779

\[\boxed{\text{779.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[3x^{2} + 2x + k = 0,\ \ \]

\[2x_{1} = - 3x_{2} \Longrightarrow x_{1} = - 1,5x_{2}\]

\[x^{2} + \frac{2}{3}x + \frac{k}{3} = 0\]

\[\left\{ \begin{matrix} x_{1} + x_{2} = - \frac{2}{3} \\ x_{1}x_{2} = \frac{k}{3}\text{\ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} - 1,5x_{2} + x_{2} = - \frac{2}{3} \\ - 1,5x_{2} \cdot x_{2} = \frac{k}{3}\text{\ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} - 0,5x_{2} = - \frac{2}{3}\ \ \ | \cdot ( - 2) \\ - 1,5x_{2}^{2} = \frac{k}{3}\ \ \ \ \ \ \ \ \ \ \ \ | \cdot 3 \\ \end{matrix} \right.\ \ \]

\[\left\{ \begin{matrix} x_{2} = \frac{4}{3}\text{\ \ \ \ \ \ \ \ \ \ } \\ k = - 4,5x_{2}^{2} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[k = - 4,5 \cdot \left( \frac{4}{3} \right)^{2} = - 4,5 \cdot \frac{16}{9} =\]

\[= - 0,5 \cdot 16 = - 8\]

\[Ответ:k = - 8\text{.\ }\]