Question

Cho A= 10²⁰²⁰ +1/ 10²⁰²¹+1 và B= 10²⁰²¹+1/ 10²⁰²²+1. Không tính kết quả, hãy so sánh A và B.

Answer 1

\(10A=\dfrac{10^{2021}+10}{10^{2021}+1}=\dfrac{\left(10^{2021}+1\right)+9}{10^{2021}+1}=\dfrac{10^{2021}+1}{10^{2021}+1}+\dfrac{9}{10^{2021}+1}=1+\dfrac{9}{10^{2021}+1}\)

\(10B=\dfrac{10^{2022}+10}{10^{2022}+1}=\dfrac{\left(10^{2022}+1\right)+9}{10^{2022}+1}=\dfrac{10^{2022}+1}{10^{2022}+1}+\dfrac{9}{10^{2022}+1}=1+\dfrac{9}{10^{2022}+1}\)

Vì \(10^{2022}>10^{2021}=>10^{2021}+1< 10^{2022}+1\)

\(=>\dfrac{9}{10^{2021}+1}>\dfrac{9}{10^{2022}+1}\)

\(=>10A>10B\)

\(=>A>B\)

Answer 2