Đáp án:
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
$\begin{array}{l}
\dfrac{y}{{x - z}} = \dfrac{{y + x}}{z} = \dfrac{x}{y}\\
= \dfrac{{y + y + x + x}}{{x - z + z + y}}\\
= \dfrac{{2.x + 2.y}}{{x + y}}\\
= \dfrac{{2.\left( {x + y} \right)}}{{x + y}}\\
= 2\\
\Rightarrow \dfrac{y}{{x - z}} = \dfrac{{y + x}}{z} = \dfrac{x}{y} = 2\\
\Rightarrow \left\{ \begin{array}{l}
x = 2.y\\
y + x = 2z
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x = 2y\\
y + 2y = 2z
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x = 2y\\
3y = 2z
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x = 2y\\
z = \dfrac{3}{2}y
\end{array} \right.\\
\Rightarrow x:y:z = \left( {2y} \right):y:\left( {\dfrac{3}{2}y} \right) = 2:1:\dfrac{3}{2}\\
Hay\,x:y:z = 4:2:3
\end{array}$
