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The value of (2023)2024+(2023)2023+2024(2023)2023+1\frac{(2023)^{2024}+(2023)^{2023}+2024}{(2023)^{2023}+1} (2023)2023+1(2023)2024+(2023)2023+2024​​is
Question

The value of (2023)2024+(2023)2023+2024(2023)2023+1\frac{(2023)^{2024}+(2023)^{2023}+2024}{(2023)^{2023}+1} ​is:

A.

2023

B.

2025

C.

2024

D.

4047

Correct option is C

Given: 

(2023)2024+(2023)2023+2024(2023)2023+1\frac{(2023)^{2024}+(2023)^{2023}+2024}{(2023)^{2023}+1}  

Solution: 

(2023)2024+(2023)2023+2024(2023)2023+1 =(2023)2023(2023+1)+2024(2023)2023+1 =(2023)2023(2024)+2024(2023)2023+1 =(2024)[(2023)2023+1](2023)2023+1 =2024\frac{(2023)^{2024}+(2023)^{2023}+2024}{(2023)^{2023}+1} \\ \ \\ =\frac{(2023)^{2023}(2023+1)+2024}{(2023)^{2023}+1}\\ \ \\ = \frac{(2023)^{2023}(2024)+2024}{(2023)^{2023}+1}\\ \ \\ = \frac{(2024)[\cancel{(2023)^{2023}+1}]}{\cancel{(2023)^{2023}+1}}\\ \ \\ = 2024​​

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