Question

So sánh A và B, biết :
A=\(\frac{20^{10}+1}{20^{10}-1}\) và B= \(\frac{20^{10}-1}{20^{10}-3}\)
Giúp mình nhá ^^ Mình tick cho, thanks nhiều :D

Answer 1

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

Nên A = B

Answer 2

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

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

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

Answer 3

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

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

Do 20¹⁰ - 1 > 20¹⁰ - 3

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

Hay A < B 

Ai thấy tớ đúng k nha