a; \(\dfrac{x}{2}\) = \(\dfrac{y}{5}\) = \(\dfrac{z}{7}\)
Áp dụng dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{2}\) = \(\dfrac{y}{5}\) = \(\dfrac{z}{7}\) = \(\dfrac{x+y+z}{2+5+7}\) = \(\dfrac{28}{14}\) = 2
\(x=\) 2.2 = 4
y = 2.5 = 10
z = 2.7 = 14
Vậy (\(x;y;z\)) = (4; 10; 14)
b; 3\(x\) = 4y; ⇒ \(x=\dfrac{4}{3}y\); 5y = 7z ⇒ z = \(\dfrac{5}{7}\)y
Thay \(x=\dfrac{4}{3}y\); z = \(\dfrac{5}{7}\)y vào biểu thức 2\(x\) - 2y + z = 18 ta có:
2.\(\dfrac{4}{3}y\) - 2y + \(\dfrac{5}{7}\)y = 18
y.(\(\dfrac{8}{3}\) - 2 + \(\dfrac{5}{7}\)) = 18
y.(\(\dfrac{2}{3}\) + \(\dfrac{5}{7}\)) = 18
y.\(\dfrac{29}{21}\) = 18
y = 18 : \(\dfrac{29}{21}\)
y =\(\dfrac{378}{29}\); \(x\) = \(\dfrac{4}{3}\).\(\dfrac{378}{29}\) = \(\dfrac{504}{29}\); z = \(\dfrac{5}{7}\).\(\dfrac{378}{29}\) = \(\dfrac{270}{29}\)
Kết luận:...
\(a,\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7}\) và \(x+y+z=28\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{x+y+z}{2+5+7}=\dfrac{28}{14}=2\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{2}=2\\\dfrac{y}{5}=2\\\dfrac{z}{7}=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2.2\\y=2.5\\z=2.7\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=4\\x=10\\z=14\end{matrix}\right.\)
Vậy .....
