Question

So sánh

A=10²⁰¹⁹+2 ------------ 10²⁰¹⁹-1 B=10²⁰¹⁹ ---------- 10²⁰¹⁹-3

Answer 1

Có: \(A=\frac{10^{2019}+2}{10^{2019}-1}=\frac{10^{2019}-1+3}{10^{2019}-1}=1+\frac{3}{10^{2019}-1}\)

\(B=\frac{10^{2019}}{10^{2019}-3}=\frac{10^{2019}-3+3}{10^{2019}-3}=1+\frac{3}{10^{2019}-3}\)

Mà \(\frac{3}{10^{2019}-1}>\frac{3}{10^{2019}-3}\)

\(\Rightarrow1+\frac{3}{10^{2019}-1}>1+\frac{3}{10^{2019}-3}\\ \Rightarrow A>B\)