Решебник по алгебре 8 класс Мерзляк ФГОС Задание 345

 

\[\boxed{\text{345\ (345).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

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

\[\frac{3^{\backslash 2(x - 5)}}{5 \cdot (x + 5)} + \frac{1^{\backslash 5(x + 5)}}{2 \cdot (x - 5)} -\]

\[- \frac{5^{\backslash 10}}{(x - 5)(x + 5)} = 0\]

\[\frac{3 \cdot 2 \cdot (x - 5) + 5 \cdot (x + 5) - 5 \cdot 10}{10 \cdot (x - 5)(x + 5)} = 0\]

\[\frac{6x - 30 + 5x + 25 - 50}{10 \cdot (x - 5)(x + 5)} = 0\]

\[\frac{11x - 55}{10 \cdot (x - 5)(x + 5)} = 0\]

\[\left\{ \begin{matrix} 11x - 55 = 0 \\ x \neq 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq - 5\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = \frac{55}{11}\ \\ x \neq 5\ \ \ \\ x \neq - 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 5\ \ \ \\ x \neq 5\ \ \ \\ x \neq - 5 \\ \end{matrix} \right.\ \]

\[Ответ:нет\ корней.\]

\[\boxed{\text{345.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \left\{ \begin{matrix} x + y = 4 \\ xy = 4\ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 4 - x\ \ \ \ \ \\ x(4 - x) = 0 \\ \end{matrix} \right.\ \]

\[x_{1} = 0;\]

\[y_{1} = 4 - x = 4;\]

\[x_{2} = 4;\]

\[y_{2} = 4 - x = 4 - 4 = 0.\]

\[Ответ:(0;4);(4;0).\]

\[2)\ \left\{ \begin{matrix} 5x + y = 0 \\ xy = 45\ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = - 5x\ \ \ \ \ \ \ \ \\ - 5x \cdot x = 45 \\ \end{matrix} \right.\ \]

\[- 5x^{2} = 45\]

\[x^{2} = - 9\]

\[Нет\ корней.\]

\[Ответ:нет\ решений.\]