\(2sin3x+1=0\Leftrightarrow sin3x=-\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=-\dfrac{\pi}{6}+k2\pi\\3x=\dfrac{7\pi}{6}+n2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{18}+\dfrac{k2\pi}{3}\\x=\dfrac{7\pi}{18}+\dfrac{n2\pi}{3}\end{matrix}\right.\)
\(x\in\left(-\dfrac{25\pi}{18};\dfrac{31\pi}{18}\right)\Rightarrow\left\{{}\begin{matrix}-\dfrac{25\pi}{18}< -\dfrac{\pi}{18}+\dfrac{k2\pi}{3}\le< \dfrac{31\pi}{18}\\-\dfrac{25\pi}{18}< \dfrac{7\pi}{18}+\dfrac{n2\pi}{3}< \dfrac{31\pi}{18}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}-2< k< \dfrac{8}{3}\\-\dfrac{8}{3}< n< 2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}k=\left\{-1;0;1;2\right\}\\n=\left\{-2;-1;0;1\right\}\end{matrix}\right.\)
\(\Rightarrow\) Pt có 8 nghiệm trên khoảng đã cho
