\(C-D=\dfrac{\left(98^{99}+1\right)\left(98^{88}+1\right)-\left(98^{89}+1\right)\left(98^{98}+1\right)}{\left(98^{89}+1\right)\left(98^{88}+1\right)}\)

\(=\dfrac{98^{187}+98^{99}+98^{88}+1-98^{197}-98^{89}-98^{98}-1}{\left(98^{89}+1\right)\left(98^{88}+1\right)}\)

\(=\dfrac{98^{99}-98^{98}+98^{88}-98^{89}}{\left(98^{89}+1\right)\left(98^{88}+1\right)}=\dfrac{98^{98}\left(98-1\right)-98^{88}\left(98-1\right)}{\left(98^{89}+1\right)\left(98^{88}+1\right)}\)

\(=\dfrac{97.98^{98}-97.98^{88}}{\left(98^{89}+1\right)\left(98^{88}+1\right)}=\dfrac{97.98^{88}\left(98^{10}-1\right)}{\left(98^{89}+1\right)\left(98^{88}+1\right)}>0\)

\(\Rightarrow C>D\)

Bài 1: 

1: \(17A=\dfrac{17^{19}+17}{17^{19}+1}=1+\dfrac{16}{17^{19}+1}\)

\(17B=\dfrac{17^{18}+17}{17^{18}+1}=1+\dfrac{16}{17^{18}+1}\)

mà \(17^{19}+1>17^{18}+1\)

nên 17A>17B

hay A>B

2: \(C=\dfrac{98^{99}+98^{10}+1-98^{10}}{98^{89}+1}=98^{10}+\dfrac{1-98^{10}}{98^{89}+1}\)

\(D=\dfrac{98^{98}+98^{10}+1-98^{10}}{98^{88}+1}=98^{10}+\dfrac{1-98^{10}}{98^{88}+1}\)

mà \(98^{89}+1>98^{88}+1\)

nên C>D

Vì C= \(\dfrac{98^{99}+1}{98^{89}+1}\)>1 thì nên áp dụng tính chất . Nên \(\dfrac{a}{b}\)>1 thì \(\dfrac{a}{b}\)>\(\dfrac{a+m}{b+m}\) ( a∈ N , b và m ∈ N^✳) Ta có : C= \(\dfrac{98^{99}+1}{98^{89}+1}\)> \(\dfrac{98^{99}+1+97}{98^{89}+1+97}\)= \(\dfrac{98^{99}+98}{98^{89}+98}\) = \(\dfrac{98.98^{98}+98.1}{98.98^{88}+98.1}\) = \(\dfrac{98.\left(98^{98}+1\right)}{98.\left(98^{88}+1\right)}\)= \(\dfrac{98^{98}+1}{98^{88}+1}\)= B ⇔ Vậy \(\dfrac{98^{99}+1}{98^{89}+1}\)< \(\dfrac{98^{89}+1}{98^{88}+1}\) nên C<D

D > C

a: \(98^{10}\cdot A=\dfrac{98^{98}+98^{10}}{98^{98}+1}=1+\dfrac{98^{10}-1}{98^{98}+1}\)

\(98^{10}\cdot B=\dfrac{98^{99}+98^{10}}{98^{99}+1}=1+\dfrac{98^{10}-1}{98^{99}+1}\)

98^88+1>98^99+1

=>A<B

b: \(\dfrac{1}{2022^2}\cdot C=\dfrac{2022^{2023}+1}{2022^{2023}+2022^2}=1+\dfrac{1-2022^2}{2022^{2023}+2022^2}\)

\(\dfrac{1}{2022^2}\cdot D=\dfrac{2022^{2021}+1}{2022^{2021}+2022^2}=1+\dfrac{1-2022^2}{2022^{2021}+2022^2}\)

2022^2023>2022^2021

=>2022^2023+2022^2>2022^2021+2022^2

=>\(\dfrac{2022^2-1}{2022^{2023}+2022^2}< \dfrac{2022^2-1}{2022^{2021}+2022^2}\)

=>\(\dfrac{1-2022^2}{2022^{2023}+2022^2}>\dfrac{1-2022^2}{2022^{2021}+2022^2}\)

=>C>D

C < D

Chắc chắn

\(C=\frac{98^{99}+1}{98^{89}+1}\)

\(D=\frac{98^{98}+1}{98^{88}+1}\)

\(C< \frac{98^{99}+1+97}{98^{89}+1+97}=\frac{98^{99}+98}{98^{89}+98}=\frac{98^{98}\left(98+1\right)}{98^{88}\left(98+1\right)}\)

\(C< \frac{98^{98}}{98^{88}}=D\)

\(C=\frac{98^{99}+1}{98^{88}+1}\)\(D=\frac{98^{98}+1}{98^{98}+1}\)

Vì C>1 còn D=1 nên C>D

dung cho mih nha