Question

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

Answer 1

\(\dfrac{3x-2y}{4}=\dfrac{2z-4x}{3}=\dfrac{4y-3z}{2}\Rightarrow\dfrac{4.\left(3x-2y\right)}{4.4}=\dfrac{3.\left(2z-4x\right)}{3.3}=\dfrac{2\left(4y-3z\right)}{2.2}\)

=\(\dfrac{12x-8y}{16}=\dfrac{6z-12x}{9}=\dfrac{8y-6z}{4}=\dfrac{0}{29}\)

\(\Rightarrow\) 12x= 8y

6z=12x

8y=6z

=> 12x=8y=6z

MSC: 24

ta có: \(\dfrac{12x}{24}=\dfrac{8y}{24}=\dfrac{6z}{24}\)= \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\)( đpcm)