Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 803

\[1)\ \frac{3x}{2x - 1} + \frac{x + 1}{x + 2} = \frac{3}{2 - 3x - 2x^{2}}\]

\[3x(x + 2) + (x + 1)(2x - 1) = - 3\]

\[3x^{2} + 6x + 2x^{2} - x + 2x - 1 = - 3\]

\[5x^{2} + 7x + 2 = 0\]

\[D = 49 - 40 = 9\]

\[x_{1} = \frac{- 7 - 3}{2 \bullet 5} = - 1;\]

\[x_{2} = \frac{- 7 + 3}{2 \bullet 5} = - 0,4.\]

\[Ответ:\ - 1;\ - 0,4.\]

\[2)\ \frac{4x^{2}}{x + 2} - \frac{10}{x + 2} + 4 = 0\ \ \ \ \ | \bullet (x + 2)\]

\[4x^{2} - 10 + 4(x + 2) = 0\]

\[4x^{2} - 10 + 4x + 8 = 0\]

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

\[2x^{2} + 2x - 1 = 0\]

\[D = 4 + 8 = 12\]

\[x = \frac{- 2 \pm \sqrt{12}}{2 \bullet 2} = \frac{- 2 \pm 2\sqrt{3}}{4} =\]

\[= \frac{- 1 \pm \sqrt{3}}{2}.\]

\[Ответ:\ \ \frac{- 1 \pm \sqrt{3}}{2}.\]