`Đáp` `án+` `Giải` `thích` `các` `bước` `giải:`
`(m-2)x^2-(2m-3)x+m-1=0`
`Để` `PT` `có` `2` `nghiệm` `phân` `biệt` `thì` `Δ>0`
`<=> (2m-3)^2-4.(m-2)(m-1) > 0`
`<=> 4m^2 - 12x+9-4m^2+12m -8 > 0`
`<=> 1 > 0 \forall m`
`Áp` `dụng` `hệ` `thức` `Vi-ét` `ta` `có`
$\begin{cases}x_1+x_2=\dfrac{3-2m}{m-2}\\x_1 x_2 = \dfrac{m-1}{m-2}\\\end{cases}$
`Ta` `có`
`x_1^2 + x_2^2 = 3x_1 x_2 -1`
`<=> (x_1 +x_2)^2 - 2x_1x_2 = 3x_1 x_2 -1`
`<=> (x_1 +x_2)^2 - 5x_1 x_2 +1=0`
`Thế` `Vi-ét` `vào` `ta` `được`
`<=> ((3-2m)/(m-2))^2 - 5. (m-1)/(m-2) + 1 =0`
`<=> (3-2m)^2 -5(m-1) + m-2 =0 (m \ne 2)`
`<=> 4m^2-12m+9 - 5m+1+m-2=0`
`<=>4m^2 -16m + 8=0`
`<=> m^2-4m+2=0`
`<=>` \(\left[ \begin{array}{l}m_1=2\\m_2=-2\end{array}(T/M) \right.\)
`Vậy` `giá` `trị` `cần` `tìm` `là` `m=+-2`
