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МатематикаРешебник по алгебре 9 класс Макарычев Задание 367
Задание 367
\[\boxed{\text{367\ (367).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \frac{1}{x^{2} - 6x + 8} - \frac{1}{x - 2} +\]
\[+ \frac{10}{x^{2} - 4} = 0\]
\[x^{2} - 6x + 8 = (x - 2)(x - 4)\]
\[D_{1} = 9 - 8 = 1\]
\[x_{1} = 3 + 1 = 4;\ \ \ x_{2} = 3 - 1 = 2.\]
\[\frac{1^{\backslash x + 2}}{(x - 4)(x - 2)} - \frac{1^{\text{(}x - 4)(x + 2)}}{x - 2} +\]
\[+ \frac{10^{\backslash x - 4}}{(x - 2)(x + 2)} = 0\]
\[\frac{x + 2 - (x - 4)(x + 2) + 10 \cdot (x - 4)}{(x - 2)(x + 2)(x - 4)} = 0\]
\[ОДЗ:\ \ \ \ x \neq 2,\ \ x \neq - 2,\ \ \]
\[x \neq 4.\]
\[x + 2 - \left( x^{2} - 2x - 8 \right) + 10x -\]
\[- 40 = 0\]
\[- x^{2} + 13x - 30 = 0\]
\[x^{2} - 13x + 30 = 0\]
\[По\ теореме\ Виета:\ \]
\[x_{1} + x_{2} = 13;\ \ x_{1} \cdot x_{2} = 30\]
\[\ x_{1} = 10;\ \ \ \ x_{2} = 3.\]
\[\textbf{б)}\ \frac{3}{x^{2} - x - 6} + \frac{3}{x + 2} = \frac{7}{x^{2} - 9}\]
\[x^{2} - x - 6 = (x + 2)(x - 3)\]
\[x_{1} + x_{2} = 1;\ \ \ x_{1} \cdot x_{2} = - 6\]
\[x_{1} = - 2;\ \ \ \ x_{2} = 3.\]
\[\frac{3^{\backslash x + 3}}{(x - 3)(x + 2)} + \frac{3^{\backslash\text{(}x - 3)(x + 3)}}{x + 2} -\]
\[- \frac{7^{\backslash x + 2}}{(x - 3)(x + 3)} = 0\]
\[\frac{3 \cdot (x + 3) + 3 \cdot \left( x^{2} - 9 \right) - 7 \cdot (x + 2)}{(x + 2)(x - 3)(x + 3)} = 0\]
\[ОДЗ:\ \ \ x \neq - 2,\ \ x \neq 3,\ \ \]
\[x \neq - 3.\]
\[3x + 9 + 3x^{2} - 27 - 7x -\]
\[- 14 = 0\]
\[3x^{2} - 4x - 32 = 0\]
\[D_{1} = 4 + 3 \cdot 32 = 100\]
\[x_{1,2} = \frac{2 \pm 10}{3} = 4;\ - \frac{8}{3}.\]
\[Ответ:а)\ 3;10;\ \ б) - 2\frac{2}{3};4.\]
\[\boxed{\text{367.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
Пояснение.
Решение.
\[x^{2} + y^{2} = r^{2} \Longrightarrow уравнение\ \]
\[окружности;(0;0) - центр\ \]
\[окружности.\]
\[\textbf{а)}\ A\ \left( - 2;\sqrt{5} \right):\]
\[( - 2)^{2} + \left( \sqrt{5} \right)^{2} = 4 + 5 = 9\]
\[x^{2} + y^{2} = 9.\]
\[\textbf{б)}\ \text{B\ }(3;4):\]
\[3^{2} + 4^{2} = 9 + 16 = 25\]
\[x^{2} + y^{2} = 25.\]
\[\textbf{в)}\ \text{C\ }(8;0):\]
\[8^{2} + 0^{2} = 64\]
\[x^{2} + y^{2} = 64.\]
