Question

So sánh A = \(\dfrac{10^{11}-1}{10^{12}-1}\) và B =\(\dfrac{10^{10}+1}{10^{11}+1}\)

Answer 1

ta có: \(A=\dfrac{10.10^{10}-1}{10.10^{11}-1}=\dfrac{10^{10}-1}{10^{11}-1}\)

so sánh: \(A=\dfrac{10^{10}-1}{10^{11}-1}\)và \(B=\dfrac{10^{10}+1}{10^{11}+1}\)

\(\Rightarrow A< B\)

Answer 2

10A=\(\dfrac{10^{12}-10}{10^{12}-1}=1-\dfrac{9}{10^{12}-1}\)

10B =\(\dfrac{10^{11}+10}{10^{11}+1}=1+\dfrac{9}{10^{11}+1}\)

\(\dfrac{9}{10^{12}-1}< \dfrac{9}{10^{12}+1}\) =>\(1-\dfrac{9}{10^{12}-1}< 1+\dfrac{9}{10^{11}+1}\)

=> 10A < 10B

=> A<B

Vậy A < B

Answer 3

\(A=\dfrac{10^{11}-1}{10^{12}-1};B=\dfrac{10^{10}+1}{10^{11}+1}\)

\(A=\dfrac{10.10^{10}-1}{10.10^{11}-1}\)và \(B=\dfrac{10^{10}+1}{10^{11}+1}\)

Vậy A<B