Question

[Nguyễn Thảo Linh]

so sánh già trị các biểu thức sau

\(A=\frac{2011\times2012}{2011+2012}+\frac{2009\times2010}{2009+2010}\)

\(B=\frac{2011\times2011}{2011+2012}+\frac{2010\times2010}{2009+2010}\)

Answer 1

[Cô Hoàng Huyền]

\(A=\frac{2011\times2012}{2011+2012}+\frac{2009\times2010}{2009+2010}\)

\(A=\frac{2011\times2011}{2011+2012}+\frac{2011}{2011+2012}+\frac{2010\times2010}{2009+2010}-\frac{2010}{2009+2010}\)

\(A=\frac{2011\times2011}{2011+2012}+\frac{2010\times2010}{2009+2010}+\frac{2011}{2011+2012}-\frac{2010}{2009+2010}\)

\(A=B+\frac{2011}{2011+2012}-\frac{2010}{2009+2010}\)

\(A=B+\frac{2011}{4023}-\frac{2010}{4019}\)

Dễ thấy \(\frac{2011}{4023}-\frac{2010}{4019}< 0\)

\(\Rightarrow A< B\)