Question

 Cmr nếu: |a|<1,|b-1|<10,|a-c|<10 thì |ab-c|<20

Answer 1

Ta có:

\(ab-c=ab-a+a-c=a\left(b-1\right)+\left(a-c\right)\)

\(\Rightarrow\left|ab-c\right|=\left|a\left(b-1\right)+\left(a-c\right)\right|\)

\(\Rightarrow\left|ab-c\right|\le\left|a\left(b-1\right)\right|+\left|a-c\right|\)

\(\Rightarrow\left|ab-c\right|\le\left|a\right|\left|b-1\right|+\left|a-c\right|\)

Mà \(\left|a\right|< 1;\left|b-1\right|< 10;\left|a-c\right|< 10\)

\(\Rightarrow\left|ab-c\right|< 1.10+10\)

\(\Rightarrow\left|ab-c\right|< 20\left(đpcm\right)\)