Ta có :A= (2005 - 4 ) x(2005 +4) =2005 x2005 -4 x4 < 2005 x 2005 hay A<B

A lớn hơn!

A= 2005x2005=2005x(1995+10)=2005x1995+20050

B=1995x(2005+10)=1995x2005+19950

vì 19950<20050 nên 1995x2005+19950<1995x2005+20050 hay b<a

A=2005x2005 > B=1995 x 2015

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

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

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 = 2008 x 2008

= (2007 + 1) x 2008

= 2007 x 2008 + 2008 x 1

= 2007 x 2008 + 2008

B = 2007 x 2009

= 2007 x (2008 +1)

= 2007 x 2008 + 2007 x 1

= 2007 x 2008 + 2007

Vì 2008 < 2007 => A > B

Ta có \(B=2007\times2009\)\(=\left(2008-1\right)\times\left(2008+1\right)\)\(=2008\times2008+2008-2008-1\)\(=2008\times2008-1\)

Vì \(-1< 0\)nên \(2008\times2008-1< 2008\times2008\)hay \(B< A\)

\(A=2008\times2008=2008^2\)

\(B=2007\times2009=\left(2008-1\right)\left(2008+1\right)=2008^2-1\)

\(\Rightarrow A>B\)

a)

\(a=2136\times2136=2136\times\left(2134+2\right)=2136\times2134+2136\times2\)

\(b=2134\times2138=2134\times\left(2136+2\right)=2134\times2136+2134\times2\)

Vì \(2136\times2>2134\times2\)     

=> \(a>b\)

b)

=> \(a=b\)\(b=123\times246+77-=123\times\left(245+1\right)+77=123\times245+123+77=123\times245+200\)\(a=245\times124-45=245\times\left(123+1\right)-45=245\times123+245-45=245\times123+200\)

Kết quả câu b là nghịch đảo kết quả câu a.

Kết quả câu c và d khác nhau. Phép chia không có tính chất giao hoán, tính chất kết hợp.

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

a lớn hơn b nhé ae

a lớn hơn b