\(\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}=\frac{3xz-2yz}{4z}=\frac{2yz-4xy}{3y}=\frac{4xy-3xz}{2x}=\frac{\left(3xz-2yz\right)+\left(2yz-4xy\right)+\left(4xy-3xz\right)}{4z+3y+2x}=0\)
\(\Rightarrow\hept{\begin{cases}3x-2y=0\\2z-4x=0\end{cases}}\Rightarrow\hept{\begin{cases}3x=2y\\2z=4x\end{cases}}\Rightarrow\hept{\begin{cases}\frac{x}{2}=\frac{y}{3}\\\frac{x}{2}=\frac{z}{4}\end{cases}\Rightarrow\frac{x}{2}=\frac{y}{3}=\frac{z}{4}}\)
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ndo81 chi ko
mở ngoặc ra và ghép các số giống nhau vào thì nó =0
\(\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}=\frac{4\left(3x-2y\right)}{4^2}=\frac{3\left(2z-4x\right)}{3^2}=\frac{2\left(4y-3z\right)}{2^2}\)
\(=\frac{4.3x-4.2y}{4^2}=\frac{3.2z-3.4x}{3^2}=\frac{2.4y-2.3z}{2^2}=\frac{4.3x-4.2y+3.2z-3.4x+2.4y-2.3z}{4^2+3^2+2^2}=0\)
\(\Rightarrow3x-2y=0.4=0\)\(\Rightarrow3x=2y\)\(\Rightarrow\frac{x}{2}=\frac{y}{3}\)(1)
\(2z-4x=0.3=0\)\(\Rightarrow2z=4x\)\(\Rightarrow\frac{x}{2}=\frac{z}{4}\)(2)
Từ (1) và (2) \(\Rightarrow\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\left(đpcm\right)\)
ta có : \(\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}\) = \(\frac{3xz-2yz}{4z}=\frac{2zy-4xy}{3y}=\frac{4yx-3zx}{2x}\)
=\(\frac{\left(3xz-2yyz\right)+\left(2zy-4xy\right)+\left(4yx-3zx\right)}{4z+3y+2x}=0\)
\(\Rightarrow\hept{\begin{cases}3x-2y=0\\2z-4x=0\\4y-3z=0\end{cases}\Rightarrow\hept{\begin{cases}3x=2y\\2z=4x\\4y=3z\end{cases}\Rightarrow}}\) \(\hept{\begin{cases}\frac{x}{2}=\frac{y}{3}\\\frac{z}{4}=\frac{x}{2}\\\frac{y}{3}=\frac{z}{4}\end{cases}\left(đpcm\right)}\)
