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2019 . 2021 - 2020. 2020
= 2019(2020+1) - 2020( 2019+1)
= 2019 .2020 + 1.2019 - 2020.2019 + 1.2020
= 2019 -2020
= -1
\(2019.2021-2020.2020\)
\(=2019\left(2020+1\right)-2020\left(2019+1\right)\)
\(=2019.2020+2019-2020.2019+2020\)
\(=2019-2020\)
\(=-1\)
Ta có: \(A=\left(2020^{2019}+2019^{2019}\right)^{2020}\)
\(=\left(2019^{2019}+2020^{2019}\right)^{2019}\cdot\left(2019^{2019}+2020^{2019}\right)\)
\(\Leftrightarrow\dfrac{A}{B}=\dfrac{\left(2019^{2019}+2020^{2019}\right)^{2019}\cdot\left(2019^{2019}+2020^{2019}\right)}{\left(2020^{2020}+2019^{2020}\right)^{2019}}\)
\(\Leftrightarrow\dfrac{A}{B}=\dfrac{2019^{2019}+2020^{2019}}{2019+2020}>1\)
\(\Leftrightarrow A>B\)
mk sai đề một tí
A=2019 mũ 2020 + 1
trên 2019 mũ 2020 - 3
B=2019 mũ 2020 -1
trên 2019mũ 2020 - 5
so sánh A và B
ta có :\(E=\frac{2019^{2019}+1}{2019^{2020}+1}\Leftrightarrow2019\cdot E=\frac{2019^{2020}+2019}{2019^{2020}+1}=1+\frac{2019}{2019^{2020}+1}\)
\(F=\frac{2019^{2020}+1}{2019^{2021}+1}\Leftrightarrow2019\cdot F=\frac{2019^{2021}+2019}{2019^{2021}+1}=1+\frac{2019}{2019^{2021}+1}\)
vì \(\frac{2019}{2019^{2020}+1}>\frac{2019}{2019^{2021}+1}\) nên E>F
E=2019 x 2019 x 2019 x ........ x 2019 x2019 +1 /2019 x 2019 x 2019 x.........x 2019 x 2019 + 1
E=1+1/2019+1
E=2/2020
E=1/1010
F=2019 x 2019 x 2019 x .......... x 2019 x 2019 +1 / 2019 x 2019 x 2019 x ....... x 2019 x 2019 +1
F= 1+1/2019+1
F=2/2020
F=1/1010
từ đó ta có E=F(=1/1010)
Tính nhanh:
2019.(2020 - 164) - 2020.(2019 - 164)
= 2019.2020 - 2019.164 - 2020.2019 + 2020 .164
= (2019.2020 - 2020.2019) - (2019.164 - 2020.164)
= 0 - 164.(2019 - 2020)
= -164.(-1)
= 164
2019.(2020 - 164) - 2020.(2019 - 164)
= 2019.2020 - 2019.164 - 2029.2019 + 2020.164
= (2019.2020 - 2020.2019) + (2020.164 - 2019.164)
= 0 + 164.(2020 - 2019)
= 164.1
= 164