Решебник по алгебре 8 класс Мерзляк ФГОС Задание 687

 

\[\boxed{\mathbf{687\ (687).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ 6x² + 5x - \frac{1}{x + 1} = 1 - \frac{1}{x + 1}\]

\[6x^{2} + 5x - \frac{1}{x + 1} - 1 + \frac{1}{x + 1} = 0,\ \ \]

\[x + 1 \neq 0;\ \ x \neq - 1\]

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

\[D = 25 + 24 = 49\]

\[x = \frac{- 5 \pm 7}{12}\]

\[x_{1} = - 1\ (не\ подходит);\ \ \ x_{2} = \frac{1}{6}\]

\[Ответ:x = \frac{1}{6}.\]

\[2)\ 5x² - 14 \cdot \left( \sqrt{x} \right)^{2} - 3 = 0\]

\[5x^{2} - 14x - 3 = 0,\ \ x \geq 0\]

\[D = 196 + 4 \cdot 15 = 256\]

\[x = \frac{14 \pm 16}{10}\]

\[x_{1} = 3;\ \ \ \ \ x_{2} = - \frac{1}{5}\ (не\ подходит)\]

\[Ответ:x = 3.\]

\[\boxed{\mathbf{6}\mathbf{8}\mathbf{7}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x² + ax + a - 4 = 0\]

\[\left\{ \begin{matrix} x_{1} = 0\ \ \ \ \ \\ a - 4 = 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x_{1} = 0 \\ a = 4\ \\ \end{matrix} \right.\ \]

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

\[x(x + 4) = 0\]

\[x_{1} = 0;\ \ x_{2} = - 4\]

\[Ответ:a = 4;\ \ x_{2} = - 4.\]

\[2)\ 4x² + (a - 8)x + a² + a = 0\]

\[Если\ a = 0:\]

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

\[4x(x - 2) = 0\ \ \]

\[x_{2} = 2.\]

\[Если\ \ a = - 1:\]

\[4x^{2} - 9x = 0\ \ \]

\[x(4x - 9) = 0\ \ \]

\[x_{2} = \frac{9}{4} = 2\frac{1}{4}.\]

\[Ответ:a = 0,\ x_{2} = 2;\ \ \ \ \]

\[a = - 1,\ x_{2} = 2\frac{1}{4}.\]

\[3)\ ax² + (a + 3)x + a² - 3a = 0\]

\[3x^{2} + 6x = 0\ \ \]

\[3x(x + 2) = 0\ \]

\[x_{2} = - 2\]

\[Ответ:a = 3;\ \ x_{2} = - 2.\]