a) Ta có: x/2=y/3=z/4
\(\Leftrightarrow\)x/2=2y/6=3z/12
Áp dụng tính chất bằng nhau ,ta có:
x/2=2y/6=3z/12=x+2y+3z/2+6+12= -20/20=-1
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{2}=-1\\\dfrac{2y}{6}=-1\\\dfrac{3z}{12}=-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=-3\\z=-4\end{matrix}\right.\)
Vậy x=-2 , y=-3 , z=-4
b) Ta có: x/2= y/3
\(\Leftrightarrow\)x/10=y/15 (1)
y/5=z/4
\(\Leftrightarrow\) y/15=z/12 (2)
Từ (1); (2) \(\Rightarrow\) x/10=y/15=z/12
Áp dụng tính chất bằng nhau ,ta có:
x/10=y/15=z/12=z-y+z/10-15+12=-49/7=-7
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{10}=-7\\\dfrac{y}{15}=-7\\\dfrac{z}{12}=-7\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-70\\y=-105\\z=-84\end{matrix}\right.\)
Vậy x=-70 , y=-105 , z=-84
c) Ta có: x/10=y/6=z/21
\(\Leftrightarrow\) 5x/50=y/6=2z/42
Áp dụng tính chất tỷ số bằng nhau,ta có:
5x/50=y/6=2z/42=5x+y-2z/50+6-42=28/16=2
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{5x}{50}=2\\\dfrac{y}{6}=2\\\dfrac{2z}{42}=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=20\\y=12\\z=42\end{matrix}\right.\)
Vậy x=20,y=12,z=42
