ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 770

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\[5x^{2} - 12x + c = 0,\ \ \]

\[x_{1} = 3x_{2}\]

\[x^{2} - \frac{12}{5}x + \frac{c}{5} = 0\]

\[\left\{ \begin{matrix} x_{1} + x_{2} = \frac{12}{5} \\ x_{1}x_{2} = \frac{c}{5}\text{\ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} 3x_{2} + x_{2} = \frac{12}{5} \\ 3x_{2} \cdot x_{2} = \frac{c}{5} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 4x_{2} = \frac{12}{5}\ \ \ |\ :4 \\ 3x_{2}^{2} = \frac{c}{5}\ \ \ \ \ \ | \cdot 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x_{2} = \frac{3}{5}\text{\ \ \ \ \ } \\ c = 15x_{2}^{2} \\ \end{matrix} \right.\ \]

\[c = 15 \cdot \left( \frac{3}{5} \right)^{2} = 15 \cdot \frac{9}{25} =\]

\[= 3 \cdot 9\ :5 = \frac{27}{5} = 5,4.\]

\[Ответ:c = 5,4.\ \]