Question

[Người ẩn danh]

10¹⁹⁸⁷+1;10¹⁹⁸⁹+1

_______;_________SO,SÁNH,HAI,PHÂN,SỐ,TRÊN

10¹⁹⁸⁸+1;10¹⁹⁹⁰+1

giúp,mình,với

Answer 1

[Nguyễn Lê Phước Thịnh]

Đặt \(A=\dfrac{10^{1987}+1}{10^{1988}+1};B=\dfrac{10^{1989}+1}{10^{1990}+1}\)

Ta có: \(A=\dfrac{10^{1987}+1}{10^{1988}+1}\)

\(\Leftrightarrow10A=\dfrac{10^{1988}+10}{10^{1988}+1}=1+\dfrac{9}{10^{1988}+1}\)

Ta có: \(B=\dfrac{10^{1989}+1}{10^{1990}+1}\)

\(\Leftrightarrow10B=\dfrac{10^{1990}+10}{10^{1990}+1}=1+\dfrac{9}{10^{1990}+1}\)

Ta có: \(10^{1988}+1< 10^{1990}+1\)

\(\Leftrightarrow\dfrac{9}{10^{1988}+1}>\dfrac{9}{10^{1990}+1}\)

\(\Leftrightarrow1+\dfrac{9}{10^{1988}+1}>1+\dfrac{9}{10^{1990}+1}\)

hay A>B