Решебник по алгебре 8 класс Мерзляк Задание 777

\[\boxed{\mathbf{777\ (777).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{x^{2} + 3x - 4}{x + 1} = 0;\ \ \ x \neq - 1\]

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

\[x_{1} + x_{2} = - 3,\ \ x_{1} = - 4\]

\[x_{1} \cdot x_{2} = - 4,\ \ x_{2} = 1\]

\[Ответ:\ x = - 4;x = 1.\]

\[2)\ \frac{x^{2} - 6x - 7}{x - 7} = 0;\ \ \ \ \ \ \ \ \ \ x \neq 7\]

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

\[x_{1} + x_{2} = 6,\ \ \]

\[x_{1} = 7\ (не\ подходит)\]

\[x_{1} \cdot x_{2} = - 7,\ \ x_{2} = - 1\]

\[Ответ:\ x = - 1.\]

\[3)\ \frac{3x^{2} - x - 2}{1 - x} = 0;\ \ \ \ \ \ x \neq 1\]

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

\[x_{1} + x_{2} = \frac{1}{3},\ \ x_{1} = - \frac{2}{3}\]

\[x_{1} \cdot x_{2} = - \frac{2}{3},\ \ \]

\[x_{2} = 1\ (не\ подходит)\]

\[Ответ:\ x = - \frac{2}{3}.\]

\[4)\ \frac{x^{2} - 8x}{x + 10} = \frac{20}{x + 10}\]

\[\frac{x^{2} - 8x - 20}{x + 10} = 0;\ \ \ \ \ \ x \neq - 10\]

\[x^{2} - 8x - 20 = 0\]

\[x_{1} + x_{2} = 8,\ \ x_{1} = 10\]

\[x_{1} \cdot x_{2} = - 20,\ \ x_{2} = - 2\]

\[Ответ:\ x = - 2;x = 10.\]

\[5)\ \frac{x^{2} - 14}{x + 2} = \frac{5x}{x + 2}\]

\[\frac{x^{2} - 14 - 5x}{x + 2} = 0;\ \ \ \ \ \ x \neq - 2\]

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

\[x_{1} + x_{2} = 5,\ \ x_{1} = 7\]

\[x_{1} \cdot x_{2} = - 14,\ \ \]

\[x_{2} = - 2\ (не\ подходит)\]

\[Ответ:x = 7.\]

\[6)\ \frac{x^{2} + 10x}{x - 8} = \frac{12x + 48}{x - 8}\]

\[\frac{x^{2} + 10x - 12x - 48}{x - 8} = 0;\ \ \ \]

\[x \neq 8\]

\[x^{2} - 2x - 48 = 0\]

\[x_{1} + x_{2} = 2,\ \ \]

\[x_{1} = 8\ (не\ подходит)\]

\[x_{1} \cdot x_{2} = - 48,\ \ x_{2} = - 6\]

\[Ответ:\ x = - 6.\]

\[7)\ \frac{x^{2} + 4x}{x - 5} - \frac{9x + 50}{x - 5} = 0\]

\[\frac{x^{2} + 4x - 9x - 50}{x - 5} = 0;\ \ \ \ \ x \neq 5\]

\[x^{2} - 5x - 50 = 0\]

\[x_{1} + x_{2} = 5,\ \ x_{1} = 10\]

\[x_{1} \cdot x_{2} = - 50,\ \ x_{2} = - 5\]

\[Ответ:\ x = - 5;x = 10.\]

\[8)\ \frac{x^{2} - 6x}{x - 3} + \frac{15 - 2x}{x - 3} = 0\]

\[\frac{x^{2} - 6x + 15 - 2x}{x - 3} = 0;\ \ \ \ x \neq 3\]

\[x^{2} - 8x + 15 = 0\]

\[x_{1} + x_{2} = 8,\ \ x_{1} = 5\]

\[x_{1} \cdot x_{2} = 15,\ \ \]

\[x_{2} = 3\ (не\ подходит)\]

\[Ответ:x = 5.\]

\[9)\ \frac{x^{2} - 6x}{x - 4} = 4\]

\[\frac{x^{2} - 6x - 4x + 16}{x - 4} = 0;\ \ \ \ \ x \neq 4\]

\[x^{2} - 10x + 16 = 0\]

\[x_{1} + x_{2} = 10,\ \ x_{1} = 8\]

\[x_{1} \cdot x_{2} = 16,\ \ x_{2} = 2\]

\[Ответ:x = 8;x = 2.\]

\[10)\ \frac{5x + 18}{x - 2} = x\]

\[\frac{5x + 18}{x - 2} - x = 0\]

\[\frac{5x + 18 - x^{2} + 2x}{x - 2} = 0;\ \ \ \ \ x \neq 2\]

\[- x^{2} + 7x + 18 = 0\]

\[x^{2} - 7x - 18 = 0\]

\[x_{1} + x_{2} = 7,\ \ x_{1} = 9\]

\[x_{1} \cdot x_{2} = - 18,\ \ x_{2} = - 2\]

\[Ответ:x = 9;\ x = - 2.\]

\[11)\ x + 1 = \frac{6}{x}\ \ \ \ \ \ \ \ | \cdot x\ \ \ \ \ \]

\[\ \ \ \ \ \ x \neq 0\]

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

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

\[x_{1} \cdot x_{2} = - 6,\ \ x_{2} = 2\]

\[Ответ:x = 2;\ x = - 3.\]

\[12)\ 5 - \frac{8}{x^{2}} = \frac{18}{x}\]

\[5 - \frac{8}{x^{2}} - \frac{18}{x} = 0\]

\[\frac{5x² - 8 - 18x}{x²} = 0;\ \ \ \ \ \ \ \ x \neq 0\]

\[5x^{2} - 18x - 8 = 0\]

\[D = 324 + 160 = 484,\ \ \]

\[x_{1,2} = \frac{18 \pm 22}{10}\]

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

\[Ответ:\ x = - 0,4;x = 4.\]