\(2x^2-\left(m+5\right)x-3m^2+10m-3=0\)
\(\Delta=[-\left(m+5\right)]^2-4\cdot2\cdot\left(-3m^2+10m-3\right)\)
\(\Delta=m^2+10m+25+24m^2-80m+24\)
\(\Delta=25m^2-70m+49\)
Phương trình có 2 nghiệm phân biệt
Khi \(25m^2-70m+49\)>0(*)
theo định lí Vi-ét có
\(x_1+x_2=\dfrac{m+5}{2}\)
\(x_1\cdot x_2=\dfrac{-3m^2+10m-3}{2}\)
Ta có:\(x_1^2+x_2^2-\left(x_1+x_2\right)+x_1\cdot x_2=4\)
⇔\(\left(x_1+x_2\right)^2-x_1\cdot x_2-\left(x_1+x_2\right)=4\)
⇔\(\left(\dfrac{m+5}{2}\right)^2-\dfrac{-3m^2+10m-3}{2}-\dfrac{m+5}{2}=4\)
⇔\(\left(m+5\right)^2-2\left(-3m^2+10m-3\right)-2\left(m+5\right)=16\)
⇔\(7m^2-12m+5=0\)
⇔\(\left[{}\begin{matrix}m=1\left(N\right)\\m=\dfrac{5}{7}\left(N\right)\end{matrix}\right.\)
Vậy m=1 hoặc m=\(\dfrac{5}{7}\)