Question

A = 2022^2023 +1/2022^2024 +1 và B 2022^2022 + 1 /2022^2023 +1

HÃY SO SÁNH HAI BIỂU THỨC TRÊN!

Answer 1

Ta có: 

\(2022A=2022\cdot\dfrac{2022^{2023}+1}{2022^{2024}+1}=\dfrac{2022^{2024}+2022}{2022^{2024}+1}=1+\dfrac{2021}{2022^{2024}+1}\) 

\(2022B=2022\cdot\dfrac{2022^{2022}+1}{2022^{2023}+1}=\dfrac{2022^{2023}+2022}{2022^{2023}+1}=1+\dfrac{2021}{2022^{2023}+1}\)

Mà: \(2022^{2024}+1>2022^{2023}+1\)

\(\Rightarrow\dfrac{2021}{2022^{2024}+1}< \dfrac{2021}{2022^{2023}+1}\)

\(\Rightarrow1+\dfrac{2021}{2022^{2024}+1}< 1+\dfrac{2021}{2022^{2023}+1}\)

\(\Rightarrow2022A< 2022B\)

\(\Rightarrow A< B\)