Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{12x-15y}{7}=\dfrac{20z-12x}{9}=\dfrac{15y-20z}{11}=\dfrac{12x-15y+20z-12x+15y-20z}{7+9+11}=0\)
\(\Rightarrow\left\{{}\begin{matrix}12x=15y\\20z=12x\\15y=20z\end{matrix}\right.\)
\(\Leftrightarrow12x=15y=20z\Rightarrow\dfrac{x}{\dfrac{1}{12}}=\dfrac{y}{\dfrac{1}{15}}=\dfrac{z}{\dfrac{1}{20}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{\dfrac{1}{12}}=\dfrac{y}{\dfrac{1}{15}}=\dfrac{z}{\dfrac{1}{20}}=\dfrac{x+y+z}{\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{20}}=\dfrac{48}{\dfrac{1}{5}}=240\)
\(\Rightarrow\left\{{}\begin{matrix}x=240.\dfrac{1}{12}\Rightarrow x=20\\y=240.\dfrac{1}{15}\Rightarrow y=16\\z=240.\dfrac{1}{20}\Rightarrow z=12\end{matrix}\right.\)
Vậy ...........................
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