`2)` `x^2+2x+3-m=0`
`Delta'=1^2-(3-m)`
`=1-3+m`
`=m-2`
Để phương trình có 2 nghiệm thì: `Delta'\geq0`
`<=>m-2\geq0`
`<=>m\geq2`
Theo hệ thức Vi - ét ta có: $\begin{cases}x_1+x_2=-2\\x_1x_2=3-m\end{cases}$
Lại có: `A=x_1^2x_2^2+2x_1x_2(x_1+x_2)+2021`
`=(x_1x_2)^2+2x_1x_2(x_1+x_2)+2021`
`=(3-m)^2+2.(-2)(3-m)+2021`
`=m^2-6m+9-4(3-m)+2021`
`=m^2-6m+9-12+4m+2021`
`=m^2-2m+2018`
`=m^2-2m+1+2017`
`=(m-1)^2+2017\geq2017`
Ta có: `m\geq2`
`=>m-1\geq1`
`=>(m-1)^2\geq1`
`=>(m-1)^2+2017\geq2018`
Vậy `A_min=2018` khi `m=2`
