Tìm x thuộc Q,biết ://x-1/+(x-2)/+x=2019

Đáp án:

\(x \in \left\{ { - 2016;\,\,674} \right\}\)

Giải thích các bước giải: \(\begin{array}{l} \left| {x - 1} \right| + \left| {x - 2} \right| + x = 2019\,\,\,\,\left( * \right)\\ TH1:\,\,\,x < 1\\ \Rightarrow \left\{ \begin{array}{l} \left| {x - 1} \right| = - x + 1\\ \left| {x - 2} \right| = - x + 2 \end{array} \right.\\ \Rightarrow \left( * \right) \Leftrightarrow - x + 1 - x + 2 + x = 2019\\ \Leftrightarrow - x = 2016\,\,\,\\ \Leftrightarrow x = - 2016\,\,\,\,\,\left( {tm} \right)\\ TH2:\,\,1 \le x < 2\\ \Rightarrow \left\{ \begin{array}{l} \left| {x - 1} \right| = x - 1\\ \left| {x - 2} \right| = - x + 2 \end{array} \right.\\ \Rightarrow \left( * \right) \Leftrightarrow x - 1 - x + 2 + x = 2019\\ \Leftrightarrow x = 2018\,\,\,\left( {ktm} \right)\\ TH3:\,\,x \ge 2\\ \Rightarrow \left\{ \begin{array}{l} \left| {x - 1} \right| = x - 1\\ \left| {x - 2} \right| = x - 2 \end{array} \right.\\ \Rightarrow \left( * \right) \Leftrightarrow x - 1 + x - 2 + x = 2019\\ \Leftrightarrow 3x = 2022\\ \Leftrightarrow x = 674.\\ Vay\,\,\,x \in \left\{ { - 2016;\,\,674} \right\}. \end{array}\)