Question

Cho : A = \(\dfrac{2009^{2010}+1}{2009^{2009}+1}\)

B = \(\dfrac{2009^{2011}-2}{2009^{2010}-2}\)

Hãy so sánh A và B

Answer 1

A=\(\dfrac{2009^{2010}+1}{2009^{2009}+1}\)

2009A=\(\dfrac{(2009^{2010}+1)+0}{2009^{2010}+1}\)

= 1+\(\dfrac{0}{2009^{2010}+1}\)= 1+0 =1

B=\(\dfrac{2009^{2011}-2}{2009^{2010}-2}\)

2009B=\(\dfrac{2009^{2011}-1}{2009^{2011}-2009}\)

=\(\dfrac{(2009^{2011}-1)-0}{2009^{2011}-2009}\)

= \(1-\dfrac{0}{2009^{2011}-2009}\)

=1-0= 1

Vì 1=1\(\Rightarrow A=B\)

Answer 2

Ta có : A = 2009^2010+1/2009^2009+1

Suy ra: 1/2009 A = 1 - 2008/2009^2010+2009 (1)

Lại có:B = 2009^2011 - 2 / 2009^2010 - 2

Suy ra : 1/2009 B = 1 + 4016/2009^2011-4018 (2)

Vì 1 - 2008/2009^2010+2009 < 1 + 4016/2009^2011-4018 (3)

Từ (1);(2) và (3) suy ra : A<B