$$\begin{gathered} \mathrm{Ta} \mathrm{có}: \mathrm{A}={\mathrm{a}}^4-2{\mathrm{a}}^{3 }+3{\mathrm{a}}^2-4\mathrm{a}+5 \\ ={\mathrm{a}}^4-2{\mathrm{a}}^{3 }+{\mathrm{a}}^{2 }+2{\mathrm{a}}^2-4\mathrm{a}+2+3 \\ =({\mathrm{a}}^4-2{\mathrm{a}}^{3 }+{\mathrm{a}}^{2 })+2({\mathrm{a}}^2-2\mathrm{a}+1)+3 \\ ={(\mathrm{a}2-\mathrm{a})}^2+2{(\mathrm{a}-1)}^2+3\mathrm{Vì} {({\mathrm{a}}^2-\mathrm{a})}^2+2{(\mathrm{a}-1)}^2\ge 0 \\ =>{({\mathrm{a}}^2-\mathrm{a})}^2+2{(\mathrm{a}-1)}^2+3\ge 3 \\ =>\mathrm{GTNN} \mathrm{của} \mathrm{A}=3 \\ \mathrm{Dấu}"=" \mathrm{xảy} \mathrm{ra} \mathrm{khi} \mathrm{và} \mathrm{chỉ} \mathrm{khi}: \\ \mathrm{a}-1=0 \\ =>\mathrm{a}=1 \\ \mathrm{Vậy} \mathrm{GTNN} \mathrm{của} \mathrm{A}=3 \mathrm{khi} \mathrm{a}=1 \end{gathered}$$