4/
a/ $\text{Pt có nghiệm}\\→Δ=6^2-4.1.(m-2)≥0\\↔36-4m+8≥0\\↔44-4m≥0\\↔4m≤44\\↔m≤11$
b/ $x_1^2+x_2^2=20\\↔x_1^2+2x_1x_2+x_2^2-2x_1x_2=20\\↔(x_1+x_2)^2-2x_1x_2\\\text{Theo Viet}:\\ \begin{cases}x_1+x_2=-6\\x_1x_2=m-2\end{cases}\\→(-6)^2-2.(m-2)=20\\↔36-2m+4=20\\↔2m=20\\↔m=10(\rm TM)\\ \text{Vậy} \, m=10$
5/
a/ $\text{Pt có nghiệm}\\→Δ=(-2)^2-4.1.(-m^2+4m-3)≥0\\↔4+4m^2-16m+12≥0\\↔4m^2-16m+16≥0\\↔(2m-4)^2≥0\\→\rm Pt \, luôn\, có\, nghiệm$
b/ $\text{Theo Viet}:\\\begin{cases}x_1+x_2=2\\x_1x_2=-m^2+4m-3\end{cases}\\x_1^2+x_2^2+x_1x_2\\=x_1^2+x_2^2+2x_1x_2-x_1x_2\\=(x_1+x_2)^2-x_1x_2\\=2^2-(-m^2+4m-3)\\=4+m^2-4m+3\\=m^2-4m+4+3\\=(m-2)^2+3\ge 3\\→\min A=3↔m-2=0\\↔m=2(\rm TM)\\\text{Vậy} m=2$
