a) \(2023^{2024}\) và \(2023^{2023}\)

vì 2024 > 2023 nên 2023²⁰²⁴ > 2023²⁰²³

Vậy 2023²⁰²⁴ > 2023²⁰²³

b) \(17^{2024}\) và \(18^{2024}\)

vì 17 < 18 nên 17²⁰²⁴ < 18 ²⁰²⁴

Vậy 17²⁰²⁴ < 18²⁰²⁴

a)>

b)<

giúp em với

\(A=\dfrac{2024^{2023}+1}{2024^{2024}+1}\)

\(2024A=\dfrac{2024^{2024}+2024}{2024^{2024}+1}=\dfrac{\left(2024^{2024}+1\right)+2023}{2024^{2024}+1}=\dfrac{2024^{2024}+1}{2024^{2024}+1}+\dfrac{2023}{2024^{2024}+1}=1+\dfrac{2023}{2024^{2024}+1}\)

\(B=\dfrac{2024^{2022}+1}{2024^{2023}+1}\)

\(2024B=\dfrac{2024^{2023}+2024}{2024^{2023}+1}=\dfrac{\left(2024^{2023}+1\right)+2023}{2024^{2023}+1}=\dfrac{2024^{2023}+1}{2024^{2023}+1}+\dfrac{2023}{2024^{2023}+1}=1+\dfrac{2023}{2024^{2023}+1}\)

Vì \(2024>2023=>2024^{2024}>2024^{2023}\)

\(=>2024^{2024}+1>2024^{2023}+1\)

\(=>\dfrac{2023}{2024^{2023}+1}>\dfrac{2023}{2024^{2024}+1}\)

\(=>A< B\)

\(#PaooNqoccc\)

dễ

-2024/2023<-1

-1<-2023/2024

=>-2024/2023<-2023/2024

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

a: \(0,75< 1\)

=>Hàm số \(y=0,75^x\) nghịch biến trên R

mà -2,3>-2,4

nên \(0,75^{-2,3}< 0,75^{-2,4}\)

b: \(\dfrac{1}{4}< 1\)

=>Hàm số \(y=\left(\dfrac{1}{4}\right)^x\) nghịch biến trên R

mà 2023<2024

nên \(\left(\dfrac{1}{4}\right)^{2023}>\left(\dfrac{1}{4}\right)^{2024}\)

c: Vì 3,5>1

nên hàm số \(y=3,5^x\) đồng biến trên R

mà 2023<2024

nên \(3,5^{2023}< 3,5^{2024}\)

a) \(\dfrac{17}{20}< \dfrac{18}{20}< \dfrac{18}{19}\Rightarrow\dfrac{17}{20}< \dfrac{18}{19}\)

b) \(\dfrac{19}{18}>\dfrac{19+2024}{18+2024}=\dfrac{2023}{2022}\Rightarrow\dfrac{19}{18}>\dfrac{2023}{2022}\)

c) \(\dfrac{135}{175}=\dfrac{27}{35}\)

\(\dfrac{13}{17}=\dfrac{26}{34}< \dfrac{26+1}{34+1}=\dfrac{27}{35}\)

\(\Rightarrow\dfrac{13}{17}< \dfrac{135}{175}\)