$1)$
$sin^{2}x + sin2x = 3- 2m$
$<=> \frac {1 - cos2x} {2} + sin2x = 3-2m$
$<=> \frac {1 - cos2x +2sin2x} {2} =3-2m$
$<=> 1-cos2x +2sin2x =6-4m$
$<=> cos2x - 2sin2x =4m-5$
Để phương trình vô nghiệm $<=> (4m-5)^{2} > 1^{2} +(-2)^{2}$
$<=> (4m-5)^{2} > 17$
$<=> |4m-5|>\sqrt {17}$
$<=>\left[ \begin{array}{l}4m-5>\sqrt {17}\\4m-5<-\sqrt{17} \end{array} \right. $
$<=>\left[ \begin{array}{l}m>\frac {\sqrt {17}}{4}+\frac{5}{4} \\m<-\frac {\sqrt {17}}{4}+\frac {5}{4} \end{array} \right. $
$2)$
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