Ta thấy \(10^{50}>10^{50}-3\)

\(\Rightarrow B=\frac{10^{50}}{10^{50}-3}>\frac{10^{50}+2}{10^{50}-3+2}=\frac{10^{50}+2}{10^{50}-1}=A\)

Vậy \(A< B\)

Mình chưa học đến đó nên mình tịt

⇒B=10501050−3 >1050+21050−3+2 =1050+21050−1 =A

Vậy 

Ta có 

\(2550^{10}=\left(51.50\right)^{10}=51^{10}.50^{10}>50^{10}.50^{10}=50^{20}\) 

Vậy\(50^{20}< 2550^{10}\)

50²⁰ và 2550¹⁰

50²⁰= (5²)¹⁰= 25¹⁰

Ta thấy 25¹⁰ và 2550¹⁰có cùng chung một số mũ nên 2550¹⁰ không cần phải tính nữa.

Vậy : 50²⁰< 2550¹⁰

Ta co :

50^20=(50²)¹⁰=2500¹⁰

Do 2500¹⁰<2550¹⁰

^Vay 50²⁰<2550¹⁰

Ta có: \(A=\frac{10^{50}+2}{10^{50}-1}=\frac{10^{50}-1+3}{10^{50}-1}=\frac{10^{50}-1}{10^{50}-1}+\frac{3}{10^{50}-1}=1+\frac{3}{10^{50}-1}\)

\(B=\frac{10^{50}}{10^{50}-3}=\frac{10^{50}-3+3}{10^{50}-3}=\frac{10^{50}-3}{10^{50}-3}+\frac{3}{10^{50}-3}=1+\frac{3}{10^{50}-3}\)

Vì \(\frac{3}{10^{50}-1}< \frac{3}{10^{50}-3}\Rightarrow1+\frac{3}{10^{50}-1}< 1+\frac{3}{10^{50}-3}\Rightarrow A< B\)

Ta có:

\(A=\frac{10^{50}+2}{10^{50}-1}=\frac{10^{50}-1+3}{10^{50}-1}=1+\frac{3}{10^{50}-1}\)

\(B=\frac{10^{50}}{10^{50}-3}=\frac{10^{50}-3+3}{10^{50}-3}=1+\frac{3}{10^{50}-3}\)

Vì \(10^{50}-1>10^{50}-3\Rightarrow\frac{3}{10^{50}-1}< \frac{3}{10^{50}-3}\)(2 phân số có cùng tử số, mẫu số của phân số nào lớn hơn thì phân  

                                                                                             số đó nhỏ hơn)

\(\Rightarrow1+\frac{3}{10^{50}-1}< 1+\frac{3}{10^{50}-3}\Rightarrow A< B\)     

\(A=\frac{10^{50}+2}{10^{50}-1}=\frac{10^{50}-1+3}{10^{50}-1}=1+\frac{3}{10^{50}-1}.\)

\(B=\frac{10^{50}}{10^{50}-3}=\frac{10^{50}-3+3}{10^{50}-3}=1+\frac{3}{10^{50}-3}.\)

Do 10⁵⁰-1 > 10⁵⁰-3 ; => \(1+\frac{3}{10^{50}-3}>1+\frac{3}{10^{50}-1}\)

=> B > A

\(A=\frac{10^{50}+2}{10^{50}-1}=\frac{10^{50}-1+3}{10^{50}-1}=\)\(\frac{10^{50}-1}{10^{50}-1}+\frac{3}{10^{50}-1}\)\(=1+\frac{3}{10^{50}-1}\)

\(B=\frac{10^{50}}{10^{50}-3}=\frac{10^{50}-3+3}{10^{50}-3}\)\(=\frac{10^{50}-3}{10^{50}-3}+\frac{3}{10^{50}-3}\)\(=1+\frac{3}{10^{50}-3}\)

Ta có: 1<3 suy ra \(10^{50}-1>10^{50}-3\)

Suy ra\(\frac{3}{10^{50}-1}< \frac{3}{10^{50}-3}\)

Suy ra \(1+\frac{3}{10^{50}-1}< 1+\frac{3}{10^{50}-3}\)

Suy ra A<B

My best friend classmate is Nga. The first reason why I her most is her nice appearance. She has long black hair and beautiful eyes. She is tall and thin enough to paripate in VN nexttop model. Not only does she have a pretty appearance but she also has good characteriss. When I feel sad, nervous or stressful, she is always by my side and encourage me to overcome difficult challenges in my life. I'M so grateful for it. Moreover, she once said that:" If oneday you feel crying, call me..I don't promise that i will make you laugh..but i can cry with you" In addition to that, we have unforgetable experience. In 1997, I was drowning when she appeared and secured me from the Death and since then, we has become closed fiends. We share a lot of things such as dreas, jobs, hobbies,.. I strongly believe that our relationship is lasting forever.

Chúc bạn học giỏi

The person that I trust the most is my best friend, Nha. She is 18 years old. She is also my English private tutor who has been teaching me for 3 years.

She is very pretty with a lovely round face and beautiful dark brown eyes. Although she is not so tall, her black hair is very long and silky. Her favorite clothes are jeans, T-shirts and sneakers for their comfort. At first, she appeared serious but  later she showed her humorous side. She always makes me laugh all the times when we see each other. She is not only good at English but she also plays piano exceptionally well. She can even compose songs. Furthermore, conscientiousness is the most beautiful personality of her. She makes people feel pleasant in her caring and understanding quality.

She is both well-qualified teacher and a precious friend to me. I hope our relationship can last long and remain stable

I really want to tell you about my friend, one of my best friend is Tuan. We were  classmate during our five years at  Da Nang University of Technology. He was a good student of my class. He has black hair and bright eyes and is very good – looking. Tuan and I had many things in common, especially, our hobbies. We both traveling, billiard, table tennis, reading book and singing.

He has a kind heart and is easy to get on with everybody. The deeper our mutual understanding becomes the more we feel closely attached to each other. We are the best pupils in our class. Tuan is always at the top. He is good at every subject, but he never shows pride in his abilities and always tries to learn harder.

Tuan’s family is not rich. His parents are farmers. He often spends most of his free time doing useful things to help his parents. I Tuan very much because of his honesty and straight forwardness. He is always ready to help his weak friends in their study; as a result, lots of friends, thanks to his whole-hearted help, have become good ones

Ta co:

         B=\(\frac{10^{30}+1}{10^{31}+1}\)<\(\frac{10^{30}+1+99}{10^{31}+1+99}\)=\(\frac{10^{30}+100}{10^{31}+100}\)=\(\frac{10^{10}\cdot\left(10^{20}+1\right)}{10^{10}\cdot\left(10^{21}+1\right)}\)=\(\frac{10^{20}+1}{10^{21}+1}\)=A

Vay A<B

Ta có: \(\dfrac{10^{50}-3}{10^{50}+1}\)<\(\dfrac{10^{50}+1}{10^{50}+1}\)<\(\dfrac{10^{50}+1}{10^{50}-3}\)

=>\(\dfrac{10^{50}-3}{10^{50}+1}\)<​\(\dfrac{10^{50}+1}{10^{50}-3}\)​

vậy (đpcm)

b) Áp dụng  tính chất

\(\frac{a}{b}< 1\Rightarrow\frac{a}{b}< \frac{a+m}{b+m}\left(m\in N\right)\)

Ta có: \(B=\frac{10^{16}+1}{10^{17}+1}< \frac{10^{16}+1+9}{10^{17}+1+9}=\frac{10^{16}+10}{10^{17}+10}=\frac{10.\left(10^{15}+1\right)}{10.\left(10^{16}+1\right)}=\frac{10^{15}+1}{10^{16}+1}=A\)

\(\Rightarrow B< A\)

\(B< 1\Rightarrow\frac{10^{16}+1}{10^{17}+1}< \frac{10^{16}+1+9}{10^{17}+1+9}=\frac{10^{16}+10}{10^{17}+10}=\frac{10\left(10^{15}+1\right)}{10\left(10^{16}+1\right)}=\frac{10^{15}+1}{10^{16}+1}=A\)

\(\Rightarrow A>B\)