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 \(A>B\)
\(2021^3=2021.2021.2021\)
Xét B bằng :
\(2020.2021.2022\)
\(=\left(2021-1\right).2021.\left(2021+1\right)\)
\(B=2021.2021.2021+2021-2021-1\)
\(=2021.2021.2021-1\)
Mà \(A=2021.2021.2021\)
\(\Rightarrow A>B\)
A = 2021^3
= 2021 . 2021. 2021
B = 2020 . 2021 . 2022
= 2020 . 2022 . 2021
Ta có : 2021 . 2021
= (2020 + 1) . 2021
= 2020 . 2021 + 1 . 2021 (1)
2020 . 2022
= 2020 . (2021 + 1)
= 2020 . 2021 + 1 . 2020 (2)
Từ (1) , (2) => 2021 . 2021 > 2020 . 2022
=> 2021 . 2021 . 2021 > 2020 . 2021 . 2022
Vậy A > B
\(B=2020.2021.2022\)
\(B=2020.2021.\left(2021+1\right)\)
\(B=2021.2021.2021+2020.2021\)
\(B=\left(2021-1\right).2021^2+2020.2021\)
\(B=2021.2021^2-2021^2+2020.2021\)
\(B=2021^3-2021\left(2021-2020\right)\)
\(B=2021^3-2021< 2021^3\)
\(A< B\)
