3x-2y/4=2z-4x/3=4y-3z/2 Chứng minh rằng x/2=y/3=y/4 AI giúp mk , mk cho 50đ

Từ đẳng thức đã cho ta có

$\dfrac{3x-2y}{4} = \dfrac{2z-4x}{3} = \dfrac{4y – 3z}{2}$

Ta có

$\dfrac{3x-2y}{4} =\dfrac{4y – 3z}{2} = \dfrac{6x-4y}{8} = \dfrac{6x-4y+4y-3z}{8+2} = \dfrac{6x-3z}{10}$

Lại có

$\dfrac{2z-4x}{3} = \dfrac{3z-6x}{\frac{9}{2}}$

Vậy ta có

$\dfrac{3z-6x}{\frac{9}{2}} = \dfrac{6x-3z}{10} = \dfrac{3z-6x+6x-3z}{10 + \frac{9}{2}} = \dfrac{0}{\frac{29}{2}} = 0$

Vậy ta suy ra

$\dfrac{3x-2y}{4} = \dfrac{2z-4x}{3} = \dfrac{4y – 3z}{2} = 0$

hay

$3x-2y = 2z-4x = 4y-3z = 0$

Do $3x – 2y = 0$ suy ra $\dfrac{x}{2} = \dfrac{y}{3}$

Do $2z-4x = 0$ suy ra $\dfrac{x}{2} = \dfrac{z}{4}$

Do $4y – 3z = 0$ suy ra $\dfrac{y}{3} = \dfrac{z}{4}$

Vậy 

$\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{4}$