Question

So sánh : \(C=\frac{20^{10}+1}{20^{10}-1}\)Và \(D=\frac{20^{10}-1}{20^{10}-3}\)

Answer 1

Ta có :\(C=\frac{20^{10}+1}{20^{10}-1}\)

=> \(C-1=\frac{20^{10}+1-\left(20^{10}-1\right)}{20^{10}-1}=\frac{2}{20^{10}-1}\)

Lại có D = \(\frac{20^{10}-1}{20^{10}-3}\)

=> D - 1 = \(\frac{20^{10}-1-\left(20^{10}-3\right)}{20^{10}-3}=\frac{2}{20^{10}-3}\)

Vì \(20^{10}-1>20^{10}-3\Rightarrow\frac{2}{20^{10}-1}< \frac{2}{2^{10}-3}\Rightarrow C-1< D-1\Rightarrow C< D\)

Answer 2

Có : \(C=\frac{20^{10}+1}{20^{10}-1}\)

< = > \(C-1=\frac{20^{10}+1-\left(20^{10}-1\right)=\frac{2}{20^{10}-1}}{20^{10}-1}\)

có D \(\frac{20^{10}-1}{20^{10}-3}\)

=> D - 1 = \(\frac{20^{10}-1\left(20^{10}-3\right)}{20^{10}-3}=\frac{2}{20^{10}-3}\)

Answer 3

\(C=\frac{20^{10}+1}{20^{10}-1}\)

\(\Rightarrow C-1=\frac{20^{10}+1-\left(20^{10}-1\right)}{20^{10}-1}=\frac{2}{20^{10}-1}\)

Có : \(D=\frac{20^{10}-1}{20^{10}-3}\)

\(\Rightarrow D-1=\frac{20^{10}-1-\left(20^{10}-3\right)}{20^{10}-3}=\frac{2}{20^{10}-3}\)

\(20^{10}-1>20^{10}-3\Rightarrow\frac{2}{20^{10}-1}< \frac{2}{2^{10}-3}\Rightarrow C-1< D-1\Rightarrow C< D\)