ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 771

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\[4x^{2} + bx - 27 = 0,\ \ \]

\[x_{1}\ :x_{2} = - 3\mathbf{\Longrightarrow}x_{1} = - 3 \cdot x_{2}\]

\[x^{2} + \frac{b}{4}x - \frac{27}{4} = 0\]

\[\left\{ \begin{matrix} x_{1} + x_{2} = - \frac{b}{4} \\ x_{1}x_{2} = - \frac{27}{4}\text{\ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\text{\ \ }\left\{ \begin{matrix} - 3x_{2} + x_{2} = - \frac{b}{4} \\ - 3x_{2} \cdot x_{2} = - \frac{27}{4} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} - 2x_{2} = - \frac{b}{x}\ \ \ \ | \cdot ( - 4) \\ - 3x_{2}^{2} = - \frac{27}{4}\ \ \ \ |\ :( - 3) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} b = 8x_{2} \\ x_{2}^{2} = \frac{9}{4} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} b = 8x_{2} \\ x_{2} = \pm \frac{3}{2} \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[при\ x_{1} = 1,5;\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \]

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

\[b_{1} = 8 \cdot 1,5 = 12;\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \]

\[\text{\ \ }b_{2} = 8 \cdot ( - 1,5) = - 12\]

\[Ответ:b = \pm 12.\ \]