Đáp án:
Áp dụng : $|a|$ + $|b|$ $≥$ $|a+b|$ dấu `" ="` khi $a.b ≥0$
$⇒$ $A = |x-2019|+|x-2018| + 2017 ≥ |x-2019|+|2018-x| + 2017 = |x-2019+2018-x| + 2017 = 2018$
Để `" = "` xảy ra thì : `(x-2019).(2018-x)` $≥$ $0$
$TH1$ . $\left \{ {{x-2019 > 0} \atop {2018-x > 0}} \right.$ $⇔$ $\left \{ {{x> 2019} \atop {x<2018}} \right.$ ($KTM$)
$TH2$ . $\left \{ {{x-2019 < 0} \atop {2018-x < 0}} \right.$ $⇔$ $\left \{ {{x< 2019} \atop {x>2018}} \right.$ $⇔$ $2018 < x < 2019$ ($TM$)
$TH3$ . $\left \{ {{x-2019 = 0} \atop {2018-x = 0}} \right.$ $⇔$ $\left \{ {{x= 2019} \atop {x=2018}} \right.$ ($TM$)
Vậy $A$ đạt $GTNN=2018$ khi $2018 ≤ x ≤ 2019$
