Question

\(\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}\)

CMR: \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)

Answer 1

\(\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}\)

\(\Rightarrow\frac{12x-8y}{16}=\frac{6z-12x}{9}=\frac{4y-3z}{4}\)

\(=\frac{12x-8y+6z-12x+8y-6z}{16+9+4}\)\(=0\)

\(\Rightarrow\frac{12x-8y}{16}=0\Rightarrow12x=8y\Rightarrow\frac{x}{y}=\frac{2}{3}\Rightarrow\frac{x}{2}=\frac{y}{3}\left(1\right)\)

\(\Rightarrow\frac{6z-12x}{9}=0\Rightarrow6z=12x\Rightarrow\frac{x}{z}=\frac{2}{4}\Rightarrow\frac{x}{2}=\frac{z}{4}\left(2\right)\)

Từ (1)&(2)=>\(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)