Giải:
Ta có:
\(x:y:z=\dfrac{2}{5}:\dfrac{3}{4}:\dfrac{1}{3}\)
\(\Leftrightarrow\dfrac{x}{\dfrac{2}{5}}=\dfrac{y}{\dfrac{3}{4}}=\dfrac{z}{\dfrac{1}{3}}\)
\(\Leftrightarrow\dfrac{x}{\dfrac{24}{60}}=\dfrac{y}{\dfrac{45}{60}}=\dfrac{z}{\dfrac{20}{60}}\)
\(\Leftrightarrow\dfrac{x}{24}=\dfrac{y}{45}=\dfrac{z}{20}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\dfrac{x}{24}=\dfrac{y}{45}=\dfrac{z}{20}=\dfrac{x-z}{24-20}=\dfrac{-4,8}{4}=-\dfrac{6}{5}\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{24}=-\dfrac{6}{5}\\\dfrac{y}{45}=-\dfrac{6}{5}\\\dfrac{z}{20}=-\dfrac{6}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{144}{5}\\y=-54\\z=-24\end{matrix}\right.\)
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Ta có:
\\(x:y:z=\\dfrac{2}{5}:\\dfrac{3}{4}:\\dfrac{1}{3}\\)
\\(\\Rightarrow\\dfrac{x}{\\dfrac{2}{5}}=\\dfrac{y}{\\dfrac{3}{4}}=\\dfrac{z}{\\dfrac{1}{3}}\\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\\(\\dfrac{x}{\\dfrac{2}{5}}=\\dfrac{y}{\\dfrac{3}{4}}=\\dfrac{z}{\\dfrac{1}{3}}=\\dfrac{x-z}{\\dfrac{2}{5}-\\dfrac{1}{3}}=\\dfrac{-4,8}{\\dfrac{1}{15}}=-72\\\\ \\Rightarrow x=\\left(-72\\right).\\dfrac{2}{5}=-28,8\\\\ y=\\left(-72\\right).\\dfrac{3}{4}=-54\\\\ z=\\left(-72\\right).\\dfrac{1}{3}=-24\\\\ \\Rightarrow x=-28,8;y=-54;z=-24\\)