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Doris
Doris

Doris

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Doris
Asked: Tháng Mười 26, 20202020-10-26T10:44:22+00:00 2020-10-26T10:44:22+00:00In: Môn Toán

So sánh: 2020^2019 + 2020^2020 và 2021^2020.

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So sánh: 2020^2019 + 2020^2020 và 2021^2020.

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    1. Khánh Gia

      Khánh Gia

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      Giakhanh
      2020-10-26T10:45:44+00:00Added an answer on Tháng Mười 26, 2020 at 10:45 sáng

      `2020^2019+2020^2020=2020^2019 . (1+2020)=2021 . 2020^2019`

      `2021^2020=2021 . 2021^2019`

      Do `0<2020<2021`

      `=> 2021 . 2020^2019<2021 . 2021^2019`

      `=> 2020^2019+2020^2020<2021^2020`

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    2. Calantha

      Calantha

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      Calantha
      2020-10-26T10:46:16+00:00Added an answer on Tháng Mười 26, 2020 at 10:46 sáng

      Đáp án:

      $2021^{2020} > 2020^{2019} + 2020^{2020}$

      Giải thích các bước giải:

      $+) \quad 2020^{2019} + 2020^{2020}$

      $= 2020^{2019} + 2020^{2019}.2020$

      $= 2020^{2019}.2021$

      $+) \quad 2021^{2020}$

      $= 2021^{2019}.2021$

      Do $2021 > 2020$

      $\to 2021^{2019} > 2020^{2019}$

      $\to 2021^{2019}.2021 > 2020^{2019}.2021$

      $\to 2021^{2020} > 2020^{2019} + 2020^{2020}$

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