x2−3mx+2m2+m−1=0a=0;b=−3b;c=2m2+m−13m±9m2−4(2m2+m−1)23m±9m2−8m2−4m+4)23m±m2−4m+423m±(m−2)223m±(m−2)2x1,2=3m±m−22X1=4m−22=2m−1X2=3m−m+22=m+1{\displaystyle {\begin{aligned}&x^{2}-3mx+2m^{2}+m-1=0\\&a=0;b=-3b;c=2m^{2}+m-1\\&{\frac {3m\pm {\sqrt {9m^{2}-4(2m^{2}+m-1)}}}{2}}\\&{\frac {3m\pm {\sqrt {9m^{2}-8m^{2}-4m+4)}}}{2}}\\&{\frac {3m\pm {\sqrt {m^{2}-4m+4}}}{2}}\\&{\frac {3m\pm {\sqrt {(m-2)^{2}}}}{2}}\\&{\frac {3m\pm (m-2)}{2}}\\&x_{1,2}={\frac {3m\pm m-2}{2}}\\&X_{1}={\frac {4m-2}{2}}=2m-1&X_{2}={\frac {3m-m+2}{2}}=m+1\\\end{aligned}}}
|2m−1|<2−2<2m−1<2{\displaystyle {\begin{aligned}&|2m-1|<2\\&-2<2m-1<2\\\end{aligned}}}
|m+1|<2−2<m+1<2{\displaystyle {\begin{aligned}&|m+1|<2\\&-2<m+1<2\\\end{aligned}}}
2m−1<22m<3m<32{\displaystyle {\begin{aligned}&2m-1<2\\&2m<3\\&m<{\frac {3}{2}}\\\end{aligned}}}
−2<m+1−3<m{\displaystyle {\begin{aligned}&-2<m+1\\&-3<m\end{aligned}}}
m+1<2m<1{\displaystyle {\begin{aligned}&m+1<2\\&m<1\\\end{aligned}}}
12<m<32{\displaystyle {\begin{aligned}{\frac {1}{2}}<m<{\frac {3}{2}}\end{aligned}}}
−3<m<1{\displaystyle \ -3<m<1}
12<m<1{\displaystyle {\frac {1}{2}}<m<1}