Có :

A = 10 - 9/10^1991+1

B = 10 - 9/10^1992+1

Vì 10^1991+1 < 10^1992+1 => 9/10^1991+1 > 9/10^1992+1

=> A < B

Tk mk nha

\(\frac{A}{10}=\frac{10^{1992}+1}{10^{1992}+10}=\frac{\left(10^{1992}+10\right)-9}{10^{1992}+10}=1-\frac{9}{10^{1992}+10}\)

\(\frac{B}{10}=\frac{10^{1993}+1}{10^{1993}+10}=\frac{\left(10^{1993}+10\right)-9}{10^{1993}+10}=1-\frac{9}{10^{1993}+10}\)

Vì \(10^{1992}+10< 10^{1993}+10\) nên \(1+\frac{9}{10^{1993}+10}>1+\frac{9}{10^{1993}+10}\)

Do đó \(A>B\)

lấy máy tính mà tính!

tất nhiên A>B

Ta viết lại A như sau:

\(A=\frac{10^{1992}+1}{10^{1991}+1}\)

\(=\frac{10^{1991}X10+1}{10^{1991}+1}\)

\(=\frac{10+1}{1}\)

\(=\frac{11}{1}\)

\(=11\)

\(\Rightarrow\frac{A}{10}=\frac{10^{1992}+1}{10^{1992}+10}=\frac{10^{1992}+10-9}{10^{1992}+10}=1-\frac{9}{10\left(10^{1991}+1\right)}\)

\(\Rightarrow\frac{B}{10}=\frac{10^{1993}+1}{10^{1993}+10}=\frac{10^{1993}+10-9}{10^{1993}+10}=1-\frac{9}{10\left(10^{1992}+1\right)}\)

Vì \(1-\frac{9}{10\left(10^{1991}+1\right)}< 1-\frac{9}{10\left(10^{1992}+1\right)}\Rightarrow A< B\)

So sánh tử và mẫu của 2 phân số với nhau.

đừng có ngu,như thế sao đc

Ta có :

\(A=\frac{10^{1992}+1}{10^{1991}+1}\)

\(\Rightarrow\frac{1}{10}A=\frac{10^{1992}+1}{10^{1992}+10}=\frac{10^{1992}+10-11}{10^{1992}+10}=1-\frac{11}{10^{1992}+10}\)

\(B=\frac{10^{1993}+1}{10^{1992}+1}\)

\(\Rightarrow\frac{1}{10}B=\frac{10^{1993}+1}{10^{1993}+10}=\frac{10^{1993}+10-11}{10^{1993}+10}=1-\frac{11}{10^{1993}+10}\)

Mà \(10^{1993}+10>10^{1992}+10\)

\(\Rightarrow\frac{11}{10^{1993}+10}< \frac{11}{10^{1992}+10}\)

\(\Rightarrow1-\frac{11}{10^{1993}+10}>1-\frac{11}{10^{1992}+10}\)

\(\Leftrightarrow\frac{1}{10}B>\frac{1}{10}A\)

\(\Rightarrow B>A\)

B > A k minh di co gi vao kb roi minh giai ki cho

A>B mình đảm bảo luôn

Ta thấy \(10^{1993}+1>10^{1992}+1\)

\(\Rightarrow B=\frac{10^{1993}+1}{10^{1992}+1}>\frac{10^{1993}+1+9}{10^{1992}+1+9}=\frac{10^{1993}+10}{10^{1992}+10}=\frac{10.\left(10^{1992}+1\right)}{10.\left(10^{1991}+1\right)}=\frac{10^{1992}+1}{10^{1991}+1}=A\)

\(\Rightarrow A< B\)

\(\frac{10^{1993}+1}{10^{1992}+1}>1\)

\(\Rightarrow\frac{10^{1993}+1}{10^{1992}+1}>\frac{10^{1993}+1+9}{10^{1992}+1+9}\)

\(\frac{10^{1993+1}}{10^{1992}+1}>\frac{10^{1993}+10}{10^{1992}+10}\)

\(\Rightarrow\frac{10^{1993}+1}{10^{1992}+1}>\frac{10^{1992}+1}{10^{1991}+1}\)

thank you.cảm ơn bạn nhưng mình thấy bài giảng này không chắc lắm!