Найдите координаты точек пересечения графиков функций: y=5x и y=6+4/(x-1).

Ответ:

\[y = 5x\ \ \ \ и\ \ \ \ y = 6 + \frac{4}{x - 1}\]

\[6 + \frac{4}{x - 1} = 5x\]

\[ОДЗ:\ \ x - 1 \neq 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \Longrightarrow x \neq 1\]

\[6 \cdot (x - 1) + 4 = 5x^{2} - 5x\]

\[6x - 6 + 4 = 5x^{2} - 5x\]

\[5x² - 11x + 2 = 0\]

\[D = b^{2} - 4ac =\]

\[= 121 - 4 \cdot 5 \cdot 2 = 121 - 40 =\]

\[= 81\]

\[x_{1} = \frac{11 + 9}{10} = \frac{20}{10} = 2\]

\[x_{2} = \frac{11 - 9}{10} = \frac{2}{10} = \frac{1}{5}\]

\[Ответ:(2;10);\ \ \left( \frac{1}{5};1 \right).\]