Giải:
Theo đề ra, ta có:
\(\left\{{}\begin{matrix}\dfrac{x}{2}=\dfrac{y}{3}\\\dfrac{y}{4}=\dfrac{z}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{8}=\dfrac{y}{12}\\\dfrac{y}{12}=\dfrac{z}{15}\end{matrix}\right.\Leftrightarrow\dfrac{x}{8}=\dfrac{y}{12}=\dfrac{z}{15}\)
Và \(x-y-z=28\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\dfrac{x}{8}=\dfrac{y}{12}=\dfrac{z}{15}=\dfrac{x-y-z}{8-12-15}=\dfrac{28}{-19}=-\dfrac{28}{19}\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=8.\left(-\dfrac{28}{19}\right)\\y=12.\left(-\dfrac{28}{19}\right)\\z=15.\left(-\dfrac{28}{19}\right)\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{244}{19}\\y=-\dfrac{336}{19}\\=-\dfrac{420}{19}\end{matrix}\right.\)
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