Đáp án:
$\begin{array}{l}
\frac{x}{y} = \frac{y}{z} = \frac{z}{t} = k \Rightarrow \left\{ \begin{array}{l}
x = k.y\\
y = k.z\\
z = k.t
\end{array} \right.\\
\Rightarrow x = k.\left( {k.z} \right) = {k^2}.k.t = {k^3}.t\\
\Rightarrow \frac{x}{t} = {k^3}\\
\Rightarrow {\left( {\frac{{x + y + z}}{{y + z + t}}} \right)^3} = {\left( {\frac{{k.y + k.z + k.t}}{{y + z + t}}} \right)^3} = {\left( {k.\frac{{y + z + t}}{{y + z + t}}} \right)^3} = {\left( {k.1} \right)^3} = {k^3}\\
\Rightarrow {\left( {\frac{{x + y + z}}{{y + z + t}}} \right)^3} = \frac{x}{t}\left( { = {k^3}} \right)
\end{array}$
