\(3x=4y=5z\Leftrightarrow\dfrac{x}{\dfrac{1}{3}}=\dfrac{y}{\dfrac{1}{4}}=\dfrac{z}{\dfrac{1}{5}}\)
Áp dụng TCDTSBN có:
\(\dfrac{x}{\dfrac{1}{3}}=\dfrac{y}{\dfrac{1}{4}}=\dfrac{z}{\dfrac{1}{5}}=\dfrac{x-y-z}{\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{5}}=\dfrac{-42}{\dfrac{-7}{60}}=360\)
\(\dfrac{x}{\dfrac{1}{3}}=360\Rightarrow x=120\\ \dfrac{y}{\dfrac{1}{4}}=360\Rightarrow y=90\\ \dfrac{z}{\dfrac{1}{5}}=360\Rightarrow z=72\)
Ta có:\(3x=4y=5z=\dfrac{x}{5}=\dfrac{y}{3}=\dfrac{z}{4}\)
Áp dụng tcdtsbn , ta có:
\(\dfrac{x}{5}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{x-y-z}{5-3-4}=\dfrac{-42}{-2}=21\)
\(\Rightarrow\left\{{}\begin{matrix}x=105\\y=63\\z=48\end{matrix}\right.\)
\(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}\)và X-y-z=-42
áp dung tính chất dãy tí số bằng nhau.
\(\dfrac{x}{3},\dfrac{y}{4},\dfrac{z}{5}\)và \(\dfrac{x-y-z}{3-4-5}\)=\(\dfrac{-42}{-6}=7\)
\(\dfrac{x}{3}\)=7 \(\dfrac{y}{4}\)=7 \(\dfrac{z}{5}\)=7
X=3x7 y=7x4 z=7x5
X=21 y=28 z=35
mình nghĩ như vây có sai đừng cười mình nhé