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\(B=2020.2021.2022=\left(2021-1\right).2021.\left(2021+1\right)=\left[\left(2021-1\right)\left(2021+1\right)\right].2021=\left(2021^2-2021+2021-1\right).2021=\left(2021^2-1\right).2021=2021^3-2021< 2021^3=A\)
vậy B<A
\(B=2020.2021.2022\\ B=\left(2021-1\right).2021.\left(2021+1\right)\\ B=\left(2021^2-1\right).2021\\ B=2021^3-2021\\ \Rightarrow A>B\)
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
\(A>\left(2021^2-1\right)\cdot2021=\left(2021-1\right)\left(2021+1\right)\cdot2021=B\)
\(A=2021^3=2021\cdot2021^2>2021\left(2021^2-1\right)=2021\left(2021\cdot2021-2021+2021-1\right)=2021\cdot\left(2021+1\right)\left(2021-1\right)=2021\cdot2022\cdot2020=B\)
B = 2020.2021.2022
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<\(2021^2\)
\(\Rightarrow2020.2021.2022< 2021^2.2021=2021^3\)
\(B=\left(2021-1\right)\left(2021+1\right).2021=\left(2021^2-1\right).2021=2021^3-2021< A\)
A < B
HT
Đặt \(2021=a\), khi đó \(A=a^3\)và \(B=a\left(a-1\right)\left(a+1\right)\)
Ta có: \(B=a\left(a-1\right)\left(a+1\right)=\left(a^2-a\right)\left(a+1\right)=a^3+a^2-a^2-a=a^3-a\)
Vì \(a>0\)nên hiển nhiên ta có \(B=a^3-a< a^3=A\)
Vậy \(A>B\)