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Ta có:
a) A = 2018 x 2020 = (2019 - 1) x (2019 + 1)
Áp dụng hằng đẳng thức thứ ba ta có:
A = 208 x 2020 = \(2019^2-1^2=2019^2-1\)
Vì \(2019^2-1< 2019^2\)
\(\Rightarrow\)A < B
b) A = \(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1^2\right)\left(2^2+1^2\right)\left(2^4+1^2\right)\left(2^8+1^2\right)\left(2^{16}+1^2\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(=2^{32}-1\)
Vì \(2^{32}-1< 2^{32}\)
\(\Rightarrow\)A < B
a) Áp dụng hàng đăng thức (a - b) (a + b) = a2 - b2
Ta có : A = 2018.2020 = (2019 - 1) (2019 + 1) = 20192 - 1
Mà B = 20192
Nên A < B
Ta có A = 2018.2020 + 2019.2021
= (2020 - 2).2020 + 2019.(2019 + 2)
= 20202 - 2.2020 + 20192 + 2.2019
= 20202 + 20192 - 2(2020 - 2019) = 20202 + 20192 - 2 = B
=> A = B
b) Ta có B = 964 - 1= (932)2 - 12
= (932 + 1)(932 - 1) = (932 + 1)(916 + 1)(916 - 1) = (932 + 1)(916 + 1)(98 + 1)(98 - 1)
= (932 + 1)(916 + 1)(98 + 1)(94 + 1)(94 - 1)
= (932 + 1)(916 + 1)(98 + 1)(94 + 1)(92 + 1)(92 - 1)
(932 + 1)(916 + 1)(98 + 1)(94 + 1)(92 + 1).80
mà A = (932 + 1)(916 + 1)(98 + 1)(94 + 1)(92 + 1).10
=> A < B
c) Ta có A = \(\frac{x-y}{x+y}=\frac{\left(x-y\right)\left(x+y\right)}{\left(x+y\right)^2}=\frac{x^2-y^2}{x^2+2xy+y^2}< \frac{x^2-y^2}{x^2+xy+y^2}=B\)
=> A < B
d) \(A=\frac{\left(x+y\right)^3}{x^2-y^2}=\frac{\left(x+y\right)^3}{\left(x+y\right)\left(x-y\right)}=\frac{\left(x+y\right)^2}{x-y}=\frac{x^2+2xy+y^2}{x-y}< \frac{x^2-xy+y^2}{x-y}=B\)
=> A < B
A = 2018^2 - 2016^2
A = (2018 - 2016)(2018 + 2016)
A = 2.4034
B = 2019^2 - 2017^2
B = (2019 - 2017)(2019 + 2017)
B = 2.4036
=> A < B
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bố mày đéo bt
a)
A = 1999.2001 = (2000-1)(2000+1)=20002-1
vì 20002 -1 < 20002 nên A<B
\(B=2020.2018=\left(2019+1\right)\left(2019-1\right)=2019^2-1< 2019^2=A\)
a) A = 20152
B = 2014.2016 = ( 2015 - 1 ) . ( 2015 + 1 ) = 20152 - 1
Vì 20152 > 20152 - 1
=> A > B
b) C = 316 - 1
D = 8. ( 32 + 1 ).( 34 + 1 ). ( 38 + 1 )
= ( 32 - 1 ).( 32 + 1 ).( 34 + 1 ). ( 38 + 1 )
= ( 34 - 1 ).( 34 + 1 ). ( 38 + 1 )
= ( 38 - 1 ) . ( 38 + 1 )
= 316 - 1
Vì 316 - 1 = 316 - 1
=> C = D
\(A=\left(2018-2016\right)\left(2018+2016\right)=2.4034\)
\(B=\left(2019-2017\right)\left(2019+2017\right)=2.4036\)
Ta thấy 4034 < 4036 nên A < B.
\(A=2018^2-2016^2=\left(2018+2016\right)\left(2018-2016\right)=4034.2\)
\(B=2019^2-2017^2=\left(2019+2017\right)\left(2019-2017\right)=4036.2\)
Vì 4036 > 4034 nên 4036 . 2 > 4034 . 2 nên B > A
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