Решебник по алгебре 8 класс Мерзляк ФГОС Задание 821

 

\[\boxed{\mathbf{821\ (821).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[Пусть\ x\ дней\ потратил\ \]

\[на\ задание\ первый\ рабочий,\ \]

\[а\ (x + 9)\ дней - второй\ \]

\[рабочий.\ \]

\[По\ условию\ известно,\ \]

\[что\ вместе\ они\ затратили\]

\[20\ дней.\]

\[Составляем\ уравнение:\]

\[\frac{1}{x} + \frac{1}{x + 9} - \frac{1}{20} = 0;\ \ \ \ \ \ x \neq 0;\ \ \ \]

\[x \neq - 9\]

\[20 \cdot (x + 9) + 20x - x(x + 9) =\]

\[= 0\]

\[20x + 180 + 20x - x^{2} - 9x = 0\]

\[- x^{2} + 31x + 180 = 0\]

\[x^{2} - 31x - 180 = 0\]

\[D = 961 + 720 = 1681\]

\[x_{1} = \frac{31 + 41}{2} = 36\ (дней) -\]

\[потратил\ первый\ рабочий.\]

\[x_{2} = \frac{31 - 41}{2} = - 5 \Longrightarrow не\ \]

\[удовлетворяет\ условию.\]

\[36 + 9 = 45\ (дней) - потратил\ \]

\[второй\ рабочий.\]

\[Ответ:36\ дней,\ 45\ дней.\]

\[\boxed{\mathbf{82}\mathbf{1}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{60}{x} - \frac{60}{x + 10} = \frac{1}{5}\]

\[\frac{60}{x} - \frac{60}{x + 10} - \frac{1}{5} = 0;\ \ \ \ \ x \neq 0;\ \ \ \]

\[x \neq 5\]

\[- x^{2} - 10x + 300 = 0\]

\[x^{2} + 10x - 300 = 0\]

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

\[x_{1}x_{2} = - 3000,\]

\[\text{\ \ }x_{1} = 50,\ \ x_{2} = - 60\]

\[Ответ:\ x = 50,\ x = - 60.\]

\[2)\ \frac{x}{x + 2} + \frac{x + 2}{x - 2} = \frac{16}{x^{2} - 4}\]

\[x^{2} - 2x + x^{2} + 4x + 4 - 16 = 0\]

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

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

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

\[x_{2} = 2\ (не\ подходит)\]

\[Ответ:\ x = - 3.\]

\[3)\ \frac{9}{x + 3} + \frac{14}{x - 3} = \frac{24}{x}\]

\[\ \frac{9}{x + 3} + \frac{14}{x - 3} - \frac{24}{x} = 0;\ \ \ \ x \neq 0;\]

\[x \neq 3;\ \ \ x \neq - 3\]

\[- x^{2} + 15x + 216 = 0\]

\[x^{2} - 15x - 216 = 0\]

\[x_{1} + x_{2} = 15,\ \ x_{1}x_{2} = - 216,\ \]

\[\ x_{1} = 24,\ \ x_{2} = - 9\]

\[Ответ:\ x = - 9;x = 24.\]

\[4)\ \frac{3x}{x^{2} - 10x + 25} - \frac{x - 3}{x^{2} - 5x} = \frac{1}{x}\]

\[\frac{3x}{(x - 5)^{2}} - \frac{x - 3}{x(x - 5)} - \frac{1}{x} = 0;\ \ \ \ \]

\[x \neq 0;\ \ x \neq 5\]

\[x^{2} + 18x - 40 = 0\]

\[x_{1} + x_{2} = - 18,\ \ x_{1}x_{2} = - 40,\ \]

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

\[Ответ:\ x = - 20;x = 2.\]