Question

Cho \(\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}\) . Chứng minh rằng : \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)

Answer 1

Ta có :

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

suy ra : \(\frac{4.\left(3x-2y\right)}{16}=\frac{3.\left(2z-4x\right)}{9}=\frac{2.\left(4y-3z\right)}{4}\)

\(=\frac{12x-8y+6z-12x+8y-6z}{29}=0\)

Vậy \(\frac{3x-2y}{4}=0\Rightarrow3x=2y\Rightarrow\frac{x}{2}=\frac{y}{3}\)( 1 )

\(\frac{2z-4x}{3}=0\Rightarrow2z=4x\Rightarrow\frac{x}{2}=\frac{z}{4}\)( 2 )

Từ ( 1 ) và ( 2 ) ta được : \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)