PT ⇔−[2sin2x+sinx−(1+m)]=0⇔2sin2x+sinx−(1+m)=0$\Delta = 5 + 4m$$\Rightarrow$ PT có nghiệm $\forall m > \frac{-5}{4}$$\Rightarrow$ nghiệm $ \sin x = \frac{-1\pm \sqrt{5+4m}}{4}để\sin x có nghiệm \in [0;\pi]$$\Rightarrow 0 \leq \sin x \leq1 \Rightarrow 0\leq \frac{-1\pm \sqrt{5+4m}}{4}\leq1 $$\Leftrightarrow 1 \leq \pm \sqrt{5+4m} \leq 5$
PT \Leftrightarrow -[2\sin^2 x + \sin x -(1+m)] = 0\Leftrightarrow 2\sin^2 x +\sin x -(1+m) =0$\Delta = 9 + 8m$$\Rightarrow$ PT có nghiệm $\forall m > \frac{-9}{8}$$\Rightarrow$ nghiệm $ \sin x = \frac{-1\pm \sqrt{9+8m}}{4}để \sin x có nghiệm \in [0;\pi]$$\Rightarrow 0 \leq \sin x \leq1 \Rightarrow 0\leq \frac{-1\pm \sqrt{9+8m}}{4}\leq1 $$\Leftrightarrow 1 \leq \pm \sqrt{9+8m} \leq 5$