45/49<2012/1809

Ta có 

\(A=\frac{2010.2010-1945}{2010.2010+65}

A = 2010 × 2011 - 1945 / 2010 × 2010 + 65

A = 2010 × 2010 + ( 2010 - 1945) / 2010 × 2010 + 65

A = 2010 × 2010 + 65 / 2010 × 2010 + 65

A = 1

B = 2001 × 2001 + 111 / 2001 × 2002 - 1890

B = 2001 × 2001 + 111 / 2001 × 2001 + ( 2001 - 1890)

B = 2001 × 2001 + 111 / 2001 × 2001 + 111

B = 1

=> A = B

b=1

a=1

a=b

:}

                                                  Bài làm  :

Ta có : 
\(+A=\frac{2010\times2011-1945}{2010\times2010+65}\)

\(A=\frac{2010\times2010+2010-1945}{2010\times2010+65}\)

\(A=\frac{2010\times2010+\left(2010-1945\right)}{2010\times2010+65}\)

\(A=\frac{2010\times2010+65}{2010\times2010+65}\)

\(A=1\)

\(+B=\frac{2001\times2001+111}{2001\times2002-1890}\)

\(B=\frac{2001\times2001+111}{2001\times2001+2001-1890}\)

\(B=\frac{2001\times2001+111}{2001\times2001+\left(2001-1890\right)}\)

\(B=\frac{2001\times2001+111}{2001\times2001+111}\)

\(B=1\)

Vậy A=B=1.

Chúc bạn học tốt !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Vì : ,2010 < 2010²
2010^{3 <}  2010⁴
2010^{49 <} 2010⁵⁰

Nên => a<b

Tớ làm trước _****
 

\(\frac{46}{45}=1+\frac{1}{45},\frac{2012}{2011}=1+\frac{1}{2011}\)

Có \(2011>45>0\Rightarrow\frac{1}{45}>\frac{1}{2011}\)

Do đó \(\frac{46}{45}>\frac{2012}{2011}\).

\(\frac{2011}{2010}>1>\frac{16}{17}\).

\(\frac{49}{45}=\frac{45+4}{45}=\frac{45}{45}+\frac{4}{45}=1+\frac{4}{45}\) 

\(\frac{61}{57}=\frac{57+4}{57}=\frac{57}{57}+\frac{4}{57}=1+\frac{4}{57}\) 

Vì \(\frac{4}{45}>\frac{4}{57}\) 

Nên \(1+\frac{4}{45}>1+\frac{4}{57}\) 

Vậy \(\frac{49}{45}>\frac{61}{57}\)

\(\frac{49}{45}=1+\frac{4}{45}\)

\(\frac{61}{57}=1+\frac{4}{57}\)

\(\Rightarrow\frac{49}{45}>\frac{61}{57}\)

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