|
|
Điều kiện: $0 < \sqrt 3 \sin \,2x - cos\,2x$
Khi đó PT đã cho tương đương
$\begin{array}{l}
(1) \Leftrightarrow \,\,\,\,\,0 < \sqrt 3 \sin \,2x - cos\,2x \le \sqrt 3 \\
\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,0 < \frac{{\sqrt 3 }}{2}\sin \,2x - \frac{1}{2}cos\,2x \le \frac{{\sqrt 3 }}{2}\\
\,\,\,\,\,\,\, \Leftrightarrow 0 < \sin \left( {2x - \frac{\pi }{6}} \right) \le \sin \,\frac{\pi }{3}\\
\,\,\,\,\,\, \Leftrightarrow \left[ \begin{array}{l}
k2\pi < 2x - \frac{\pi }{6} \le \frac{\pi }{3} + k2\pi \\
\frac{{2\pi }}{3} + k2\pi \le 2x - \frac{\pi }{6} < \pi + k2\pi
\end{array} \right.\,\,\,\,\,\,\,\,\,\,,\,\,\,\,(k \in Z)\\
\,\,\,\,\, \Leftrightarrow \left[ \begin{array}{l}
\frac{\pi }{{12}} + k\pi < x \le \frac{\pi }{4} + k\pi \\
\frac{{5\pi }}{{12}} + k\pi \le x < \frac{{7\pi }}{{12}} + k\pi
\end{array} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,(k \in Z)
\end{array}$
Vậy BPT đã cho có nghiệm $\left[ \begin{array}{l}
\frac{\pi }{{12}} + k\pi < x \le \frac{\pi }{4} + k\pi \\
\frac{{5\pi }}{{12}} + k\pi \le x < \frac{{7\pi }}{{12}} + k\pi
\end{array} \right.(k\in Z)$
|