Найдите координаты точек пересечения графиков функций: y=4x и y=7/(x+1)-1.

Ответ:

\[y = 4x\ \ \ \ \ \ и\ \ \ y = \frac{7}{x + 1} - 1\]

\[4x = \frac{7}{x + 1} - 1\]

\[ОДЗ:\ \ x \neq - 1\]

\[4x = \frac{7 - x - 1}{x + 1}\]

\[4x(x + 1) = 6 - x\]

\[4x^{2} + 4x - 6 + x = 0\]

\[4x^{2} + 5x - 6 = 0\]

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

\[= 25 - 4 \cdot 4 \cdot ( - 6) =\]

\[= 25 + 96 = 121\]

\[x_{1} = \frac{- 5 + 11}{8} = \frac{6}{8} = \frac{3}{4}\]

\[x_{2} = \frac{- 5 - 11}{8} = - \frac{16}{8} = - 2\]

\[y_{1} = 4 \cdot \frac{3}{4} = 3\]

\[y_{2} = 4 \cdot ( - 2) = - 8\]

\[Ответ:\left( \frac{3}{4};\ \ 3 \right);\ \ \ ( - 2; - 8).\]