$\begin{array}{l} y = \dfrac{{2\sin 2x + \cos 2x}}{{\sin 2x - \cos 2x + 3}}\\ \Leftrightarrow y\sin 2x - y\cos 2x + 3y = 2\sin 2x + \cos 2x\\ \Leftrightarrow \left( {y - 2} \right)\sin 2x - \left( {y + 1} \right)\cos 2x = - 3y\\ \Rightarrow pt\,\,co\,\,nghiem \Leftrightarrow {\left( {y - 2} \right)^2} + {\left( {y + 1} \right)^2} \ge 9{y^2}\\ \Leftrightarrow {y^2} - 4y + 4 + {y^2} + 2y + 1 \ge 9{y^2}\\ \Leftrightarrow 7{y^2} + 2y - 5 \le 0\\ \Leftrightarrow - 1 \le y \le \frac{5}{7}\\ y \in Z \Rightarrow y \in \left\{ { - 1;\,\,0} \right\}\\ \Rightarrow y\,\,nhan\,\,\,2\,\,gia\,\,tri\,\,nguyen. \end{array}$
