$\dfrac{6x}{1}=\dfrac{9y}{2}=\dfrac{12z}{3}$
$→\dfrac{x}{\dfrac{1}{6}}=\dfrac{y}{\dfrac{2}{9}}=\dfrac{z}{\dfrac{1}{4}}$
$→\dfrac{x²}{\dfrac{1}{36}}=\dfrac{y²}{\dfrac{4}{81}}=\dfrac{z²}{\dfrac{1}{16}}$
$→\dfrac{x²}{\dfrac{1}{36}}=\dfrac{2y²}{\dfrac{8}{81}}=\dfrac{3z²}{\dfrac{3}{16}}$
Áp dụng tính chất dãy tỉ số bằng nhau:
$\dfrac{x²}{\dfrac{1}{36}}=\dfrac{2y²}{\dfrac{8}{81}}=\dfrac{3z²}{\dfrac{3}{16}}=\dfrac{x²+2y²+3z²}{\dfrac{1}{36}+\dfrac{8}{81}+\dfrac{3}{16}}=\dfrac{1}{\dfrac{407}{1296}}=\dfrac{1296}{407}$
$→\begin{cases}x²=\dfrac{36}{407}\\y²=\dfrac{64}{407}\\z²=\dfrac{81}{407}\end{cases}$
$→\begin{cases}x=±\dfrac{6}{\sqrt{407}}\\y=±\dfrac{8}{\sqrt{407}}\\z=±\dfrac{9}{\sqrt{407}}\end{cases}$
