Решебник по алгебре 9 класс Мерзляк Задание 165

 

\[\boxed{\text{165\ (165).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ 6x - 5x^{2} = 0\]

\[x(6 - 5x) = 0\]

\[\left\{ \begin{matrix} x = 0\ \ \ \ \ \ \ \ \ \ \\ 6 - 5x = 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} x = 0 \\ 6 = 5x \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} x = 0 \\ x = \frac{6}{5} \\ \end{matrix} \right.\ \]

\[Ответ:x = 0;x = 1,2.\]

\[2)\ 25x^{2} = 81\]

\[x^{2} = \frac{81}{25}\]

\[x = \pm \frac{9}{5}\]

\[x = \pm 1,8\]

\[Ответ:\ x = \pm 1,8.\]

\[3)\ 4x^{2} - 7x - 2 = 0\]

\[D = 49 + 32 = 81\]

\[x = \frac{7 \pm 9}{8}\]

\[x = 2;\ \ \ \ \ x = - \frac{1}{4}\]

\[Ответ:\ x = - \frac{1}{4};\ \ x = 2.\]

\[4)\ 3x^{2} + 8x - 3 = 0\]

\[D = 64 + 36 = 100\]

\[x = \frac{- 8 \pm 10}{6}\]

\[x = - 3;\ \ \ \ x = \frac{1}{3}\]

\[Ответ:\ x = - 3;x = \frac{1}{3}.\]

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

\[D = 1 + 48 = 49\]

\[\ x = \frac{- 1 \pm 7}{2}\]

\[x = - 4;\ \ x = 3\]

\[Ответ:\ x = - 4;x = 3.\]

\[6)\ 2x^{2} + 6x + 7 = 0\]

\[D = 36 - 56 = - 20 < 0\]

\[Ответ:корней\ нет.\ \ \]

\[\boxed{\text{165.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \left\{ \begin{matrix} y = x + 2 \\ xy = 8\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} y = x + 2 \\ y = \frac{8}{x}\text{\ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]

\[y = x + 2\]

\[y = \frac{8}{x}\]

\[Ответ:( - 4;\ - 2);\ \ (2;4).\]

\[2)\ \left\{ \begin{matrix} x + y = 3\ \ \ \\ x^{2} + y^{2} = 9 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} y = 3 - x\ \ \\ x^{2} + y^{2} = 9 \\ \end{matrix} \right.\ \]

\[y = 3 - x\]

\[x^{2} + y^{2} = 9\]

\[\text{O\ }(0;0),\ \ r = 3\]

\[Ответ:(0;3);\ \ (3;0).\]