Question

Cho A=\(\frac{20^{10}+1}{20^{10}-1}\)  và B=\(\frac{20^{10}-1}{20^{10}-3}\)

So sánh A và B

Answer 1

ta có:\(A=\frac{20^{10}+1}{20^{10}-1}=\frac{20^{10}-1+2}{20^{10}-1}=\frac{20^{10}-1}{20^{10}-1}+\frac{2}{20^{10}-1}=1+\frac{2}{20^{10}-1}\)

\(B=\frac{20^{10}-1}{20^{10}-3}=\frac{20^{10}-3+2}{20^{10}-3}=\frac{20^{10}-3}{20^{10}-3}+\frac{2}{20^{10}-3}=1+\frac{2}{20^{10}-3}\)

vì 20¹⁰-1>20¹⁰-3

=>\(\frac{2}{20^{10}-1}<\frac{2}{20^{10}-3}\)

\(\Rightarrow1+\frac{2}{20^{10}-1}<1+\frac{2}{20^{10}-3}\)

=>A<B

Answer 2

Theo đề, ta có:

           \(B=\frac{20^{10}-1}{20^{10}-3}<\frac{20^{10}-1+2}{20^{10}-3+2}\)

Suy ra  \(B<\frac{20^{10}+1}{20^{10}-1}\)

Mà \(A=\frac{20^{10}+1}{20^{10}-1}\)

Nên ​​​B < A