cho 2(x+y)=5(y+x)=3(z+x).Chứng minh x-y/4=y-z/5

Ta có:

$2(x+y) = 5(y+z) = 3(z+x)$

$+) \quad 2(x+y) = 3(z+x)$

$\to \dfrac{x+y}{3} = \dfrac{z+x}{2}$

$\to \dfrac{x+y}{3} = \dfrac{z+x}{2} = \dfrac{x +y – z -x}{3 – 2} = \dfrac{y-z}{1} = y -z$

$\to \dfrac{z+x}{2} = y – z$

$\to \dfrac{z+x}{10} = \dfrac{y-z}{5}\qquad (1)$

$+) \quad 5(y+z) = 3(z+x)$

$\to \dfrac{y+z}{3} = \dfrac{z+x}{5}$

$\to \dfrac{y+z}{3} = \dfrac{z+x}{5} = \dfrac{z+x- y- z}{5 – 3} = \dfrac{x-y}{2}$

$\to \dfrac{z+x}{5} = \dfrac{x-y}{2}$

$\to \dfrac{z+x}{10} = \dfrac{x-y}{4}\qquad (2)$

$(1)(2)\to \dfrac{x-y}{4} = \dfrac{y-z}{5}$