x 2 − 3 m x + 2 m 2 + m − 1 = 0 a = 0 ; b = − 3 b ; c = 2 m 2 + m − 1 3 m ± 9 m 2 − 4 ( 2 m 2 + m − 1 ) 2 3 m ± 9 m 2 − 8 m 2 − 4 m + 4 ) 2 3 m ± m 2 − 4 m + 4 2 3 m ± ( m − 2 ) 2 2 3 m ± ( m − 2 ) 2 x 1 , 2 = 3 m ± m − 2 2 X 1 = 4 m − 2 2 = 2 m − 1 X 2 = 3 m − m + 2 2 = 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}}}
| 2 m − 1 | < 2 − 2 < 2 m − 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}}}
2 m − 1 < 2 2 m < 3 m < 3 2 {\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 < 2 m < 1 {\displaystyle {\begin{aligned}&m+1<2\\&m<1\\\end{aligned}}}
1 2 < m < 3 2 {\displaystyle {\begin{aligned}{\frac {1}{2}}<m<{\frac {3}{2}}\end{aligned}}}
− 3 < m < 1 {\displaystyle \ -3<m<1}
1 2 < m < 1 {\displaystyle {\frac {1}{2}}<m<1}
