Алгебра
Английский
Биология
География
Геометрия
Русский
История
Обществознание
Физика
Химия
Информатика
Литература
МатематикаГДЗ по алгебре 8 класс Макарычев ФГОС Задание 800
Задание 800
\[\boxed{\text{800.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
|
\[\textbf{а)}\ y = \frac{5x - 7}{x^{2} + 1} = - 6\ \ \ \ \ \ \ | \cdot \left( x^{2} + 1 \right)\text{\ \ \ \ }\] \[5x - 7 = - 6x^{2} - 6\] \[6x^{2} + 5x - 1 = 0\] \[D = 25 + 24 = 49\] \[x_{1,2} = \frac{- 5 \pm 7}{12}\] \[x_{1} = \frac{- 5 - 7}{12} = - 1;\] \[x_{2} = \frac{- 5 + 7}{12} = = \frac{1}{6}\] \[Ответ:x = - 1;\ \ x = \frac{1}{6}.\] |
\[y = \frac{5x - 7}{x^{2} + 1} = 0\] \[5x - 7 = 0\] \[5x = 7\] \[x = \frac{7}{5}\] \[Ответ:при\ x = 1,4.\] |
|---|---|
|
\[y = \frac{5x - 7}{x^{2} + 1} = 0,8\ \ \ \ \ \ \ | \cdot \left( x^{2} + 1 \right)\] \[5x - 7 = 0,8x^{2} + 0,8\] \[0,8x^{2} - 5x + 7,8 = 0\ \ \ \ \ \ |\ :0,8\] \[x^{2} - 6,25x + 9,75 = 0\] \[D = 39,0625 - 39 = 0,0625 = {0,25}^{2}\] \[x_{1,2} = \frac{6,25 \pm 0,25}{2} = \frac{6,5}{2};\frac{6}{2}\] \[x_{1} = 3,25;\ \ x_{2} = 3\] \[Ответ:при\ x = \left\{ 3;3,25 \right\}.\] |
\[y = \frac{5x - 7}{x^{2} + 1} = 0,56\ \ \ \ \ \ \ | \cdot \left( x^{2} + 1 \right)\] \[5x - 7 = 0,56x^{2} + 0,56\] \[0,56x^{2} - 5x + 7,56 = 0\ \ \ \ \ | \cdot 100\] \[56x^{2} - 500x + 756 = 0\] \[D = 250000 - 169344 = 80656 = 284^{2}\] \[x_{1,2} = \frac{500 \pm 284}{112} = 7;\frac{216}{112}\] \[x_{1} = 7;\ \ x_{2} = \frac{27}{14}\] \[Ответ:x = \left\{ 1\frac{13}{14};7 \right\}.\] |
|
\[\textbf{б)}\ y = \frac{x^{2} - 2x + 6}{x + 4} = 1,5\ \ \ \ \ \ | \cdot (x + 4)\] \[x + 4 \neq 0,\ \ x \neq - 4\] \[x^{2} - 2x + 6 = 1,5x + 6\] \[x^{2} - 3,5x = 0\] \[x(x - 3,5) = 0\] \[x = 0,\ \ x = 3,5\] \[Ответ:при\ x = \left\{ 0;3,5 \right\}.\] |
\[y = \frac{x^{2} - 2x + 6}{x + 4} = 3\ \ \ \ | \cdot (x + 4)\] \[x + 4 \neq 0,\ \ x \neq - 4\] \[x^{2} - 2x + 6 = 3x + 12\] \[x^{2} - 5x - 6 = 0\] \[D = 25 + 24 = 49\] \[x_{1,2} = \frac{5 \pm 7}{2} = 6;\ - 1\] \[Ответ:при\ x = \left\{ - 1;6 \right\}.\] |
|---|---|
|
\[y = \frac{x^{2} - 2x + 6}{x + 4} = 7\ \ \ \ | \cdot (x + 4)\] \[x + 4 \neq 0,\ \ x \neq - 4\] \[x^{2} - 2x + 6 = 7x + 28\] \[x^{2} - 9x - 22 = 0\] \[D = 81 + 88 = 169\] \[x_{1,2} = \frac{9 \pm 13}{2} = 11; - 2\] \[Ответ:при\ x = \left\{ - 2;11 \right\}\text{.\ }\] |
