Построив в одной системе координат графики функций y=8/x и y=-x^2+6x-5, определите количество корней уравнения –x^2+6x-5=8/x.

Question

Accepted Answer

\[y = \frac{8}{x}\]

\[x\]	\[\pm 2\]	\[\pm 4\]
\[y\]	\[\pm 4\]	\[\pm 2\]

\[y = - x^{2} + 6x - 5 \Longrightarrow ветви\ \]

\[вниз.\ \]

\[x_{0} = \frac{- 6}{- 2} = 3\]

\[y_{0} = - 9 + 18 - 5 = 4 \Longrightarrow \ \ (3;4)\text{.\ }\]

\[x\]	\[0\]	\[1\]
\[y\]	\[- 5\]	\[0\]

\[- x^{2} + 6x - 5 = \frac{8}{x} \Longrightarrow имеет\ \]

\[3\ корня.\]

\[Ответ:3.\]