Question

Giả xử x = \(\frac{a}{m};y=\frac{b}{m}\left(a,b,m\in Z,m>0\right)\) và x < y. Hãy chứng minh

Nếu chọn z = \(\frac{a+b}{2m}\) thì x < z < y

Answer 1

Ta có:

x = \(\frac{a}{m}\)\(\Rightarrow\)x = \(\frac{2a}{2m}\Rightarrow\)x = \(\frac{a+a}{2m}\)

y = \(\frac{b}{m}\Rightarrow\)y = \(\frac{2b}{2m}\Rightarrow\)y = \(\frac{b+b}{2m}\)

Mà x < y \(\Rightarrow\) a < b \(\Rightarrow\)a + a < b + b

Vì a + a < b + b \(\Rightarrow\)\(\frac{a+a}{2m}\) < \(\frac{a+b}{2m}\) < \(\frac{b+b}{2m}\Rightarrow\)\(\frac{a}{m}\)< \(\frac{a+b}{m}\) < \(\frac{b}{m}\)

Vậy x < z < y