Question

Cho : \(\dfrac{3x-2y}{4}\) = \(\dfrac{2z-4x}{3}\) = \(\dfrac{4y-3z}{4}\) C/m : \(\dfrac{x}{2}\) = \(\dfrac{y}{3}\) = \(\dfrac{z}{4}\)

Answer 1

Từ giả thiết \(\dfrac{3x-2y}{4}=\dfrac{2z-4x}{3}=\dfrac{4y-3z}{4}\)

\(\Rightarrow\dfrac{3xz-2yz}{4z}=\dfrac{2yz-4xy}{3y}=\dfrac{4xy-3xz}{4x}\)

Áp dung tính chất của dãy tỉ số bằng nhau, ta có :

\(\dfrac{3xz-2yz}{4z}=\dfrac{2yz-4xy}{3y}=\dfrac{4xy-3xz}{4x}=\dfrac{3xz-2yz+2yz-4xy+4xy-3xz}{4z+3y+4x}=\dfrac{0}{4z+3y+4x}=0\)

\(\Rightarrow3xz=2yz=4xy\)

\(\Rightarrow\dfrac{3xyz}{y}=\dfrac{2xyz}{x}=\dfrac{4xyz}{z}\)

\(\Rightarrow\dfrac{3}{y}=\dfrac{2}{x}=\dfrac{4}{z}\)

\(\Rightarrow\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\)(đpcm)