Question

So sánh:

A= 2005^2-2004/2005^3+1 VÀ B = 2005^2+2006/2005^3-1

giải chi tiết nha.

Answer 1

Giải:

\(A=\dfrac{2005^2-2004}{2005^3+1}\)

\(\Leftrightarrow A=\dfrac{2005^2-2005+1}{\left(2005+1\right)\left(2005^2-2005+1\right)}\)

\(\Leftrightarrow A=\dfrac{1}{2005+1}\left(1\right)\)

\(B=\dfrac{2005^2+2006}{2005^3-1}\)

\(\Leftrightarrow B=\dfrac{2005^2+2005+1}{\left(2005-1\right)\left(2005^2+2005+1\right)}\)

\(\Leftrightarrow B=\dfrac{1}{2005-1}\left(2\right)\)

Ta có:

\(\left(1\right)< \left(2\right)\)

\(\Leftrightarrow A< B\)

Vậy ...