Đáp án:
\(pt\,\,\,co\,\,2\,\,\,nghiem\,\,\,x \in \left[ {0;\,\,\frac{\pi }{2}} \right]\,\,\,la:\,\,\,\,x \in \left\{ {\frac{\pi }{6};\,\,\frac{\pi }{2}} \right\}\)
Hướng dẫn giải chi tiết:
\[\begin{array}{l}
2{\sin ^2}x - 3\sin x + 1 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin x = 1\\
\sin x = \frac{1}{2}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \frac{\pi }{2} + k2\pi \\
x = \frac{\pi }{6} + m2\pi \\
x = \frac{{5\pi }}{6} + l2\pi
\end{array} \right.\,\,\,\left( {k,\,\,m,\,\,l \in Z} \right)\\
0 \le x \le \frac{\pi }{2} \Rightarrow \left[ \begin{array}{l}
0 \le \frac{\pi }{2} + k2\pi \le \frac{\pi }{2}\\
0 \le \frac{\pi }{6} + m2\pi \le \frac{\pi }{2}\\
0 \le \frac{{5\pi }}{6} + l2\pi \le \frac{\pi }{2}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
- \frac{\pi }{2} \le k2\pi \le 0\\
- \frac{\pi }{6} \le m2\pi \le \frac{\pi }{3}\\
- \frac{{5\pi }}{6} \le l2\pi \le - \frac{\pi }{3}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
- \frac{1}{4} \le k \le 0\\
- \frac{1}{{12}} \le m \le \frac{1}{6}\\
- \frac{5}{{12}} \le l \le - \frac{1}{6}
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
k = 0\\
m = 0\\
l \in \emptyset
\end{array} \right.\\
\Rightarrow pt\,\,\,co\,\,2\,\,\,nghiem\,\,\,x \in \left[ {0;\,\,\frac{\pi }{2}} \right]\,\,\,la:\,\,\,\,x \in \left\{ {\frac{\pi }{6};\,\,\frac{\pi }{2}} \right\}.
\end{array}\]
