Ta có:\(\frac{x}{4}=\frac{2y}{5}=\frac{5z}{6}\Leftrightarrow\frac{x}{4.10}=\frac{2y}{5.10}=\frac{5z}{6.10}\Leftrightarrow\frac{x}{40}=\frac{y}{25}=\frac{z}{12}\)
\(\Leftrightarrow\frac{x^2}{1600}=\frac{y^2}{625}=\frac{z^2}{144}\Leftrightarrow\frac{x^2}{1600}=\frac{3y^2}{1875}=\frac{2z^2}{288}=\frac{x^2-3y^2+2z^2}{1600-1875+288}=\frac{325}{13}=25\)
\(\Rightarrow\hept{\begin{cases}\frac{x^2}{1600}=25\\\frac{y^2}{625}=25\\\frac{z^2}{144}=25\end{cases}\Rightarrow\hept{\begin{cases}x^2=40000\\y^2=15625\\z^2=3600\end{cases}\Rightarrow}\hept{\begin{cases}x=\pm200\\y=\pm125\\z=\pm60\end{cases}}}\)
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