Tìm x biết 2018 .|x-1| + (x-1)^2 = 2019 .|1-x|

Đáp án:

\(\left[ \begin{array}{l}
x = 1\\
x = 2\\
x = 0
\end{array} \right.\)

Giải thích các bước giải:

\(\begin{array}{l}
2018.\left| {x – 1} \right| + {\left( {x – 1} \right)^2} = 2019.\left| {1 – x} \right|\\
 \to {\left( {x – 1} \right)^2} = 2019.\left| {x – 1} \right| – 2018.\left| {x – 1} \right|\\
 \to {\left( {x – 1} \right)^2} = \left| {x – 1} \right|\\
 \to \left[ \begin{array}{l}
{\left( {x – 1} \right)^2} = \left( {x – 1} \right)\\
{\left( {x – 1} \right)^2} =  – \left( {x – 1} \right)
\end{array} \right.\\
 \to \left[ \begin{array}{l}
\left( {x – 1} \right)\left( {x – 1 – 1} \right) = 0\\
\left( {x – 1} \right)\left( {x – 1 + 1} \right) = 0
\end{array} \right.\\
 \to \left[ \begin{array}{l}
x – 1 = 0\\
x – 2 = 0\\
x = 0
\end{array} \right.\\
 \to \left[ \begin{array}{l}
x = 1\\
x = 2\\
x = 0
\end{array} \right.
\end{array}\)