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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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