Đáp án: x=2017 thì C đạt GTNN là C=2018/2019
Giải thích các bước giải:
$\begin{array}{l}
C = \frac{{\left| {x - 2017} \right| + 2018}}{{\left| {x - 2017} \right| + 2019}}\\
= \frac{{\left| {x - 2017} \right| + 2019 - 1}}{{\left| {x - 2017} \right| + 2019}}\\
= 1 - \frac{1}{{\left| {x - 2017} \right| + 2019}}\\
Ta\,co:\left| {x - 2017} \right| \ge 0\forall x\\
\Rightarrow \left| {x - 2017} \right| + 2019 \ge 2019\forall x\\
\Rightarrow \frac{1}{{\left| {x - 2017} \right| + 2019}} \le \frac{1}{{2019}}\forall x\\
\Rightarrow - \frac{1}{{\left| {x - 2017} \right| + 2019}} \ge - \frac{1}{{2019}}\forall x\\
\Rightarrow 1 - \frac{1}{{\left| {x - 2017} \right| + 2019}} \ge 1 - \frac{1}{{2019}}\forall x\\
hay\,C \ge \frac{{2019 - 1}}{{2019}}\forall x\\
\Rightarrow C \ge \frac{{2018}}{{2019}}\forall x\\
\Rightarrow GTNN\,:C = \frac{{2018}}{{2019}}\\
Dấu = xảy\,ra \Leftrightarrow \left| {x - 2017} \right| = 0\\
\Rightarrow x = 2017
\end{array}$
Vậy x=2017 thì C đạt GTNN C=2018/2019
