Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 579

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

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

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

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

\[2x = \frac{7}{2}\]

\[x = \frac{7}{4} = 1\frac{3}{4}\]

\[x = 1,75\]

\[Ответ:\ \ 1,75.\]

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

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

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

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

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

\[2x + 2 = - 3\]

\[2x = - 5\]

\[x = - \frac{5}{2} = - 2\frac{1}{2}\]

\[x = - 2,5\]

\[Ответ:\ \ x = - 2,5.\]