Question

A=2010^2011+1/2010^2012+1

B=2010^2010+1/2010^2011+1

SO SANH A VA B

 

Answer 1

A = 2010²⁰¹¹+1/ 2010²⁰¹²+1 < 2010²⁰¹¹+1 + 2009 / 2010²⁰¹²+1+2009

                                             = 2010²⁰¹¹+2010/2010²⁰¹²+2010

                                              =2010(2010^2010+1) / 2010(2010^2011+1)

                                                 = 2010^2010 + 1 / 2010^ 2011 +1 = B

=> A < B

Như vậy mới đúng nè

Answer 2

A < B nhé!

Answer 3

Ta có B=2010^2010 + 1/ 2010^2011 + 1 < 2010^2010+1+9/2010^2011+1+9=2010^2011+1/2010^2012+1 

Vậy B<A

Answer 4

ta có:\(2010A=\frac{10\left(2010^{2011}+1\right)}{2010^{2012}+1}=\frac{2010^{2012}+2010}{2010^{2012}+1}=\frac{2010^{2012}+1+2009}{2010^{2012}+1}=\frac{2010^{2012}+1}{2010^{2012}+1}+\frac{2009}{2010^{2012}+1}=1+\frac{2009}{2010^{2012}+1}\)

\(2010B=\frac{10\left(2010^{2010}+1\right)}{2010^{2011}+1}=\frac{2010^{2011}+2010}{2010^{2011}+1}=\frac{2010^{2011}+1+2009}{2010^{2011}+1}=\frac{2010^{2011}+1}{2010^{2011}+1}+\frac{2009}{2010^{2011}+1}=1+\frac{2009}{2010^{2011}+1}\)

vì 2010²⁰¹²+1>2010²⁰¹¹+1

=>\(\frac{2009}{2010^{2012}+1}<\frac{2009}{2010^{2011}+1}\)

\(\Rightarrow1+\frac{2009}{2010^{2012}+1}<1+\frac{2009}{2010^{2011}+1}\)

=>A<B