Đáp án: `x ∈ { 2017 ; 2018 }`
Giải thích các bước giải:
Ta có: `|x - 2016| + |x - 2017| + |x - 2018| + |x - 2019|`
`= (|x - 2016| + |x - 2019|) + (|x - 2017| + |x - 2018|)`
`= (|x - 2016| + |2019 - x|) + (|x - 2017| + |2018 - x|)`
`≥ |x - 2016 + 2019 - x| + |x - 2017 + 2018 - x| = 3 + 1 = 4`
Dấu "=" xảy ra `⇔` $\left\{ \begin{array}{l}(x - 2016)(2019 - x) ≥ 0\\(x - 2017)(2018 - x) ≥ 0\end{array} \right.$
`⇔` $\left\{ \begin{array}{l}(x - 2016)(x - 2019) ≤ 0\\(x - 2017)(x - 2018) ≤ 0\end{array} \right.$
Mà $\left\{ \begin{array}{l}x - 2016 > x - 2019\\x - 2017 > x - 2018\end{array} \right.$
`⇔` $\left\{ \begin{array}{l}\left\{ \begin{array}{l}x - 2016 ≥ 0\\x - 2019 ≤ 0\end{array} \right.\\\left\{ \begin{array}{l}x - 2017 ≥ 0\\x - 2018 ≤ 0\end{array} \right.\end{array} \right.$
`⇔` $\left\{ \begin{array}{l}2016 ≤ x ≤ 2019\\2017 ≤ x ≤ 2018\end{array} \right.$
`⇔ 2017 ≤ x ≤ 2018`
Mà `x ∈ ZZ` `-> x ∈ { 2017 ; 2018 }`
