Giải thích các bước giải:
Đặt:
\[\begin{array}{l}
\frac{a}{{2016}} = \frac{b}{{2017}} = \frac{c}{{2018}} = t\\
\Rightarrow \left\{ \begin{array}{l}
a = 2016t\\
b = 2017t\\
c = 2018t
\end{array} \right.\\
\Rightarrow {\left( {a - c} \right)^3} = {\left( {2016t - 2018t} \right)^3} = {\left( { - 2t} \right)^3} = - 8{t^3}\\
8{\left( {a - b} \right)^2}\left( {b - c} \right) = 8{\left( {2016t - 2017t} \right)^2}\left( {2017t - 2018t} \right) = 8.{\left( { - t} \right)^2}.\left( { - t} \right) = - 8{t^3}\\
\Rightarrow {\left( {a - c} \right)^3} = 8{\left( {a - b} \right)^2}\left( {b - c} \right)
\end{array}\]
