x – 2023 ^ (x + 1) – x – 2023 ^ (x + 2023) = 0

2 bình luận về “x – 2023 ^ (x + 1) – x – 2023 ^ (x + 2023) = 0”

1. Giải đáp:

    (x-2023)^{x+1}-(x-2023)^{x+2023}=0

   =>(x-2023)^{x}.(x-2023)^{1}-(x-2023)^{x}.(x-2023)^{2023}=0

   =>(x-2023)^{x}.(x-2023)^{1}.[1-(x-2023)^{2022}]=0

   =>(x-2023)^{x+1}.[1-(x-2023)^{2022}]=0

   Ta xét 2TH:

   +)TH1: (x-2023)^{x+1}=0

   =>x-2023=0

   =>x=2023

   +)TH2: 1-(x-2023)^{2022}=0

   =>-(x-2023)^{2022}=-1

   =>(x-2023)^{2022}=1

   =>(x-2023)^{2022}=1^{2022}=(-1)^{2022}

   =>x-2023=1 hoặc x-2023=-1

   =>x=2024 hoặc x=2022

   Vậy x\in{2022;2023;2024}

    

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2. (x –  2023)^(x + 1) – (x – 2023)^(x + 2023) = 0

   <=> (x – 2023)^(x + 1) [1 – (x – 2023)^(2022)] = 0

   <=> (x – 2023)^(x + 1) = 0 hoặc 1 – (x – 2023)^(2022) = 0

   <=> x – 2023 = 0 hoặc (x – 2023)^(2022) = 1

   <=> x= 2023 hoặc x – 2023 = 1 hoặc x – 2023 = -1

   <=> x=  2023 hoặc x = 2024 hoặc x=  2022

   Vậy x \in {2022,2023,2024}

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