Đáp án:
GTNN A=2017
Giải thích các bước giải:
$\begin{array}{l}
A = {x^4} - 2{x^3} + 3{x^2} - 4x + 2019\\
= \left( {{x^4} - 2{x^3} + {x^2}} \right) + 2{x^2} - 4x + 2019\\
= {x^2}\left( {{x^2} - 2x + 1} \right) + \left( {2{x^2} - 4x + 2} \right) + 2017\\
= {x^2}{\left( {x - 1} \right)^2} + 2\left( {{x^2} - 2x + 1} \right) + 2017\\
= {x^2}{\left( {x - 1} \right)^2} + 2{\left( {x - 1} \right)^2} + 2017\\
co\,{\left( {x - 1} \right)^2} \ge 0\forall x\\
\Rightarrow {x^2}{\left( {x - 1} \right)^2} + 2{\left( {x - 1} \right)^2} \ge 0\forall x\\
\Rightarrow {x^2}{\left( {x - 1} \right)^2} + 2{\left( {x - 1} \right)^2} + 2017 \ge 2017\forall x\\
nen\,GTNN\,cua\,A = 2017\\
dau\, = \,xay\,ra\, \Leftrightarrow x - 1 = 0 \Rightarrow x = 1
\end{array}$
