Giải thích các bước giải:
Đặt \(\dfrac{x}{{2018}} = \dfrac{y}{{2019}} = \dfrac{z}{{2020}} = k\), ta có:
\(\begin{array}{l}
\dfrac{x}{{2018}} = \dfrac{y}{{2019}} = \dfrac{z}{{2020}} = k \Rightarrow \left\{ \begin{array}{l}
x = 2018k\\
y = 2019k\\
z = 2020k
\end{array} \right.\\
{\left( {x - z} \right)^2} = {\left( {2018k - 2020k} \right)^2} = {\left( { - 2k} \right)^2} = 4{k^2}\\
4.\left( {x - y} \right)\left( {y - z} \right) = 4.\left( {2018k - 2019k} \right)\left( {2019k - 2020k} \right) = 4.\left( { - k} \right).\left( { - k} \right) = 4{k^2}\\
\Rightarrow {\left( {x - z} \right)^2} = 4.\left( {x - y} \right)\left( {y - z} \right)
\end{array}\)
