Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 754

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\[1)\arccos(2x + 3) = \frac{\pi}{3}\]

\[\arccos(2x + 3) = \arccos\frac{1}{2}\]

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

\[4x + 6 = 1\]

\[4x = - 5\]

\[x = - \frac{5}{4}.\]

\[Ответ:\ \ x = - \frac{5}{4}.\]

\[2)\arccos(3x + 1) = \frac{\pi}{2}\]

\[\arccos(3x + 1) = \arccos 0\]

\[3x + 1 = 0\]

\[3x = - 1\]

\[x = - \frac{1}{3}.\]

\[Ответ:\ \ x = - \frac{1}{3}.\]

\[3)\arccos\frac{x + 1}{3} = \frac{2\pi}{3}\]

\[\arccos\frac{x + 1}{3} = \pi - \frac{\pi}{3}\]

\[\arccos\frac{x + 1}{3} = \arccos\left( - \frac{1}{2} \right)\]

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

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

\[2x + 2 = - 3\]

\[2x = - 5\]

\[x = - \frac{5}{2}.\]

\[Ответ:\ \ x = - 2,5.\]

\[4)\arccos\frac{2x - 1}{3} = \pi\]

\[\arccos\frac{2x - 1}{3} = \arccos( - 1)\]

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

\[2x - 1 = - 3\]

\[2x = - 2\]

\[x = - 1.\]

\[Ответ:\ \ x = - 1.\]