a: \(B=\dfrac{154}{155+156}+\dfrac{155}{155+156}\)

\(\dfrac{154}{155}>\dfrac{154}{155+156}\)

\(\dfrac{155}{156}>\dfrac{155}{155+156}\)

=>154/155+155/156>(154+155)/(155+156)

=>A>B

b: \(C=\dfrac{2021+2022+2023}{2022+2023+2024}=\dfrac{2021}{6069}+\dfrac{2022}{6069}+\dfrac{2023}{6069}\)

2021/2022>2021/6069

2022/2023>2022/2069

2023/2024>2023/6069

=>D>C

Lời giải:

$b^2=ac\Rightarrow \frac{b}{a}=\frac{c}{b}$

Đặt $\frac{b}{a}=\frac{c}{b}=k\Rightarrow b=ak; c=bk$

Khi đó:
$\frac{a^{2022}+b^{2022}}{b^{2022}+c^{2022}}=\frac{a^{2022}+(ak)^{2022}}{b^{2022}+(bk)^{2022}}$

$=\frac{a^{2022}(1+k^{2022})}{b^{2022}(1+k^{2022})}=\frac{a^{2022}}{b^{2022}} (1)$

Và:

$(\frac{a+b}{b+c})^{2022}=(\frac{a+ak}{b+bk})^{2022}$

$=[\frac{a(k+1)}{b(1+k)}]^{2022}=(\frac{a}{b})^{2022}=\frac{a^{2022}}{b^{2022}}(2)$

Từ $(1); (2)$ ta có đpcm.

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

tổng 2 số là 2022 x 2 = 4044

số lớn là  ( 4044 - 2022 ) : 2 = 1011

vậy đáp án là b nhé

( đây là bài toán lớp 4 )

Câu " C " nha

Tổng hai số là: 2022 x 2 = 4044

số lớn là : ( 4044 + 2022 ) : 2 = 3033

Đ/s : tự nha

Nguyễn Thị Mai sai rồi