\(\dfrac{12x-15y}{7}=\dfrac{20z-12x}{9}=\dfrac{15y-20z}{11}\)
Theo tính chất dãy tỉ số bằng nhau:
\(\Rightarrow\dfrac{12x-15y+20z-12x+15y-20z}{7+9+11}=\dfrac{0}{27}=0\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{12x-15y}{7}=0\\\dfrac{20z-12x}{9}=0\\\dfrac{15y-20z}{11}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}12x=15y\\20z=12x\\15y=20z\end{matrix}\right.\)
\(\Rightarrow12x=15y=20z\)\(\Rightarrow\dfrac{x}{\dfrac{1}{12}}=\dfrac{y}{\dfrac{1}{15}}=\dfrac{z}{\dfrac{1}{20}}\left(1\right)\)
Áp dụng tính chất dãy tỉ số bằng nhau cho (1) ta được:
\(\dfrac{x}{\dfrac{1}{12}}=\dfrac{y}{\dfrac{1}{15}}=\dfrac{z}{\dfrac{1}{20}}=\dfrac{x+y+z}{\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{20}}=\dfrac{48}{\dfrac{1}{5}}=240\)
\(\Rightarrow\left\{{}\begin{matrix}x=240\cdot\dfrac{1}{12}=20\\y=240\cdot\dfrac{1}{15}=16\\z=240\cdot\dfrac{1}{20}=12\end{matrix}\right.\)
