Question

So sánh

A=\(\dfrac{10^{15}-9}{10^{15}-3}\)

và B=\(\dfrac{10^{16}-8}{10^{16}-2}\)

Answer 1

Ta có A = \(\dfrac{10^{15}-3-6}{10^{15}-3}\)= \(\dfrac{10^{15}-3}{10^{15}-3}-\dfrac{6}{10^{15}-3}=1-\dfrac{6}{10^{15}-3}\)

B = \(\dfrac{10^{16}-2-6}{10^{16}-2}=\dfrac{10^{16}-2}{10^{16}-2}-\dfrac{6}{10^{16}-2}\)= \(1-\dfrac{6}{10^{16}-2}\)

Vì \(10^{15}-3\) = \(\overline{100...00}-3=\overline{9...7}\) (1)

\(10^{16}-2=\overline{100...000}-2=\overline{9...8}\) (2)

Từ (1) và (2) =>\(10^{15}-3< 10^{16}-2\) hay \(\dfrac{6}{10^{15}-3}>\dfrac{6}{10^{16}-2}\)

Vậy A > B