a/ \(\frac{x}{2}=\frac{y}{4}\)
\(\Rightarrow\frac{x^2}{4}=\frac{y^2}{16}=\frac{x^2+y^2}{20}=\frac{2000}{20}=100\)
\(\Rightarrow\orbr{\begin{cases}x=-20\\x=20\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}y=-40\\y=40\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}z=-50\\z=50\end{cases}}\)
b/ \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2y-4}{6}=\frac{3z-9}{12}=\frac{x-2y+3z-1+4-9}{2-6+12}=1\)
\(\Rightarrow\hept{\begin{cases}x=3\\y=5\\z=7\end{cases}}\)
c/ \(\hept{\begin{cases}xy=6\\yz=12\end{cases}}\)
\(\Rightarrow\frac{z}{x}=\frac{12}{6}=2\)
\(\Rightarrow z=2x\)
Thế vô \(x-z=-2\) được
\(x-2x=-2\)
\(\Leftrightarrow x=2\)
\(\Rightarrow\hept{\begin{cases}z=4\\y=3\end{cases}}\)