Cho A = 20213 và B = 2020.2021.2022 Không tính cụ thể các giá trị của A và B, hãy so sánh A và B. ai trả lời giúp mình v...

A=20213=2021⋅20212>2021(20212−1)=2021(2021⋅2021−2021+2021−1)=2021⋅(2021+1)(2021−1)=2021⋅2022⋅2020=B

HT

Vậy \(A< B\)

A= 2021³= 2021.2021.2021

  =2021.[ 2021.(2020+1)]

   =2021.(2020.2021+2021)

B=2020.2021.2022

  =2021.(2020.2022)

  =2021.[2020.(2021+1)]

  =2021.(2020.2021+2020)

\(A=2021^3=2021\cdot2021^2>2021\left(2021^2-1\right)=2021\left(2021\cdot2021-2021+2021-1\right)=2021\cdot\left(2021+1\right)\left(2021-1\right)=2021\cdot2022\cdot2020=B\)

\(B=2020.2021.2022=\left(2021-1\right).2021.\left(2021+1\right)=\left[\left(2021-1\right)\left(\left(2021+1\right)\right)\right].2011=\left(2021^2-1\right).2021=2021^3-2021 2021^3=A\)

\(B=2020.2021.2022=\left(2021-1\right).2021.\left(2021+1\right)=\left[\left(2021-1\right)\left(2021+1\right)\right].2021=\left(2021^2-2021+2021-1\right).2021=\left(2021^2-1\right).2021=2021^3-2021 2021^3=A\)

vậy B

\(B=2020.2021.2022\\ B=\left(2021-1\right).2021.\left(2021+1\right)\\ B=\left(2021^2-1\right).2021\\ B=2021^3-2021\\ \Rightarrow A>B\)

Tham khảo:https://hoc24.vn/cau-hoi/cho-a-20213-va-b-202020212022-khong-tinh-cu-the-cac-gia-tri-cua-a-va-b-hay-so-sanh-a-va-b-ai-lam-giup-mik-voi.3007463332171

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Namdz

21 mon 12 2023 - olm

B = 2020.2021.2022

B = (2021 - 1).(2021 + 1).2021

B = (2021.2021 + 2021 - 2021 - 1).2021

B = (2021²⁰²¹-1).2021

B = 2021³ - 2021

Vậy A > B

2020.2022=(2021−1)(2021+1)=20212−1<\(2021^2\)

\(\Rightarrow2020.2021.2022 2021^2.2021=2021^3\)

20212 điều này là \(2021^2\) nha!