Алгебра
Английский
Биология
География
Геометрия
История
Русский
Обществознание
Физика
Химия
Информатика
Литература
МатематикаРешебник по алгебре 8 класс Макарычев ФГОС Задание 538
Задание 538
\[\boxed{\text{538\ (538).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ x^{2} - 6x = 5x - 18\]
\[x^{2} - 11x + 18 = 0\]
\[D = 121 - 72 = 49\]
\[x_{1,2} = \frac{11 \pm \sqrt{49}}{2} = \frac{11 \pm 7}{2}\]
\[x_{1} = \frac{4}{2} = 2;\ \ x_{2} = \frac{18}{2} = 9\]
\[Ответ:при\ x = 2;\ \ x = 9.\]
\[\textbf{б)}\ 3x^{2} - 4x + 3 = x^{2} + x + 1\]
\[2x^{2} - 5x + 2 = 0\]
\[D = 25 - 16 = 9\]
\[x_{1,2} = \frac{5 \pm \sqrt{9}}{2 \cdot 2} = \frac{5 \pm 3}{4}\]
\[x_{1} = \frac{2}{4} = \frac{1}{2} = 0,5;\ \ x_{2} = \frac{8}{4} = 2\ \ \ \]
\[Ответ:при\ x = 0,5;\ \ \ x = 2.\]
\(\boxed{\text{538.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\)
Пояснение.
Решение.
\[\textbf{а)}\ 8x^{2} - 14x + 5 = 0\]
\[D_{1} = 49 - 40 = 9\]
\[x_{1,2} = \frac{7 \pm \sqrt{9}}{8} = \frac{7 \pm 3}{8}\]
\[x_{1} = \frac{10}{8} = \frac{5}{4} = 1,25;\ \ \]
\[x_{2} = \frac{4}{8} = \frac{1}{2} = 0,5\]
\[Ответ:x = 1,25;\ \ x = 0,5.\]
\[\textbf{б)}\ 12t^{2} + 16t - 3 = 0\]
\[D_{1} = 64 + 36 = 100\]
\[t_{1,2} = \frac{- 8 \pm \sqrt{100}}{12} = \frac{- 8 \pm 10}{12}\]
\[t_{1} = - \frac{18}{12} = - \frac{3}{2} = - 1,5;\ \]
\[\ t_{2} = \frac{2}{12} = \frac{1}{6}\]
\[Ответ:t = - 1,5;\ \ t = \frac{1}{6}.\]
\[\textbf{в)}\ 4p^{2} + 4p + 1 = 0\]
\[D_{1} = 4 - 4 = 0\]
\[p = - \frac{2}{4} = - 0,5\]
\[Ответ:p = - 0,5.\]
\[\textbf{г)}\ x^{2} - 8x - 84 = 0\]
\[D_{1} = 16 + 84 = 100\]
\[x_{1,2} = \frac{4 \pm \sqrt{100}}{1} = 4 \pm 10\]
\[x_{1} = 14;\ \ x_{2} = - 6\]
\[Ответ:x = - 6;\ \ x = 14.\]
\[\textbf{д)}\ m^{2} + 6m - 19 = 0\]
\[D_{1} = 9 + 19 = 28 = 2\sqrt{7}\]
\[m_{1,2} = \frac{- 3 \pm 2\sqrt{7}}{1} = - 3 \pm 2\sqrt{7}\]
\[Ответ:m = - 3 \pm 2\sqrt{7}.\]
\[\textbf{е)}\ 5y^{2} + 26y - 24 = 0\]
\[D_{1} = 169 + 120 = 289\]
\[y_{1,2} = \frac{- 13 \pm \sqrt{289}}{5} = \frac{- 13 \pm 17\ }{5}\]
\[y_{1} = - 6;\ \ y_{2} = \frac{4}{5} = 0,8\]
\[Ответ:y = - 6;\ \ y = 0,8.\]
\[\textbf{ж)}\ z^{2} - 34z + 289 = 0\]
\[D = 289 - 289 = 0\]
\[z = \frac{17}{1} = 17\]
\[Ответ:z = 17.\]
\[\textbf{з)}\ 3x^{2} + 32x + 80 = 0\]
\[D = 256 - 240 = 16\]
\[x_{1,2} = \frac{- 16 \pm \sqrt{16}}{3} = \frac{- 16 \pm 4}{3}\]
\[x_{1} = - \frac{20}{3} = - 6\frac{2}{3};\ \]
\[\ x_{2} = - \frac{12}{3} = - 4\ \ \]
\[Ответ:x = - 6\frac{2}{3};\ \ x = - 4.\]
