Bài làm
\(A=\frac{m^{2010}+1}{m^{2011}+1};B=\frac{m^{2011}+1}{m^{2012}+1}\)
Ta có:
\(A=\frac{m^{2010}+1}{m^{2011}+1}\Rightarrow10A=\frac{m^{2011}+10}{m^{2011}+1}\)
\(B=\frac{m^{2011}+1}{m^{2012}+1}\Rightarrow10B=\frac{m^{2012}+10}{m^{2012}+1}\)
Hay ta so sánh: \(\frac{9}{m^{2011}};\frac{9}{m^{2012}}\)
Vì \(2011< 2012\)nên \(m^{2011}< m^{2012}\)hay \(\frac{9}{m^{2011}}>\frac{9}{m^{2012}}\)
Vậy \(A>B\)
Mình nhầm 1 chỗ chỉnh lại hộ mình phần cuối là
=> mA > mB => A>B nhé
*Sửa*
\(A=\frac{m^{2010}+1}{m^{2011}+1} \)
\(m.A = \frac{m^{2011}+(1.m)}{m^{2011}+1}=\frac{m^{2011}+m}{m^{2011}+1} = \frac{m^{2011}+1}{m^{2011}+1}+\frac{m-1}{m^{2011}+1}= 1 +\frac{m-1}{m^{2011}+1} \)
Tương tự như vậy với B
\(B=\frac{m^{2011}+1}{m^{2012}+1}; m.B= 1+\frac{m-1}{m^{2012}+1}\)
\(Vì \frac{m-1}{m^{2011}+1} > \frac{m-1}{m^{2012}+1}\)
Vậy m.A > m.B hay A > B
