Question

[Trường Nguyễn Xuân]

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

Answer 1

[Tiểu Ma Bạc Hà]

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

=>\(\frac{4\left(3x-2y\right)}{16}=\frac{3\left(2z-4y\right)}{9}=\frac{2\left(4y-3z\right)}{4}\)

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

+, \(\frac{12x-8y}{16}=0\)=>\(12x-8y=0\)=>\(12x=8y\Rightarrow3x=2y\Rightarrow\frac{x}{2}=\frac{y}{3}\left(1\right)\)

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

+, \(\frac{8y-6z}{4}=0\Rightarrow8y-6z=0\Rightarrow8y=6z\Rightarrow4y=3z\Rightarrow\frac{y}{3}=\frac{z}{4}\left(3\right)\)

Từ (1) , (2) và (3) ta suy ra : \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)(đpcm)

Answer 2

[Bùi Minh Nguyệt]

Cam on