a = 2011.2013

a = 2011.(2012+1)

a = 2011.2012 + 2011

b = 2012.2012

b = (2011+1).2012

b = 2011.2012 + 2012

Vì 2011 < 2012

=> 2011.2012 + 2011 < 2011.2012 + 2012

=> a < b

Gọi số 1987656 là a

Ta có:

\(A=\left(a+1\right).\left(a-1\right)\)

\(A=a^2-1+a-1\)

\(A=a^2+a-\left(1-1\right)\)

\(A=a^2+a\)

\(B=a.a\)

\(B=a^2\)

Vì \(a^2+a>a^2\Rightarrow A>B\)

A=(1987656+1). 1987655

A=1987656.1987655+1987655

B=(1987655+1).1987656+1987656

suy ra 1978656.1987655=1987656 và 1987655<1987656 nên A<B

\(10A=\dfrac{10^{2021}+10}{10^{2021}+1}=\dfrac{\left(10^{2021}+1\right)+9}{10^{2021}+1}=\dfrac{10^{2021}+1}{10^{2021}+1}+\dfrac{9}{10^{2021}+1}=1+\dfrac{9}{10^{2021}+1}\)

\(10B=\dfrac{10^{2022}+10}{10^{2022}+1}=\dfrac{\left(10^{2022}+1\right)+9}{10^{2022}+1}=\dfrac{10^{2022}+1}{10^{2022}+1}+\dfrac{9}{10^{2022}+1}=1+\dfrac{9}{10^{2022}+1}\)

Vì \(10^{2022}>10^{2021}=>10^{2021}+1< 10^{2022}+1\)

\(=>\dfrac{9}{10^{2021}+1}>\dfrac{9}{10^{2022}+1}\)

\(=>10A>10B\)

\(=>A>B\)

A > B nhé

Bạn trình bày bài giải cho mình nhé

Ta có:

\(A=1999\times1999=1999\times\left(1997+2\right)=1999\times1997+1999\times2\)

\(B=1997\times2001=1997\times\left(1999+2\right)=1999\times1997+1997\times2\)

Vì \(1999\times1997+1999\times2>1999\times1997+1997\times2\)Nên \(A>B\)

A=8,6x8,9=8,6x(8,8+0,1)=8,6x8,8+8,7

B=8,7x8,8=(8,6+0,1)x8,8=8,6x8,8+8,9

Vì 8,7<8,9

=>A<B

Ta có: \(B=2020.2021.2022=\left(2021-1\right).\left(2021+1\right).2021=\left(2021-1\right)^2.2021< 2021^2.2021=A\)

a = 18,18x2525,25

a = 18x1,01 x 25 x 101,01

a = 18x25x1,01x101,01

b = 25,25 x 1818,18

b = 25x1,01x18x 101,01

b = 18x25x1,01x101,01

Vậy a = b