Question

Tìm Min:

\(\frac{x^2-2x+2007}{2007x^2}\)

Answer 1

\(\frac{x^2-2x+2007}{2007x^2}\ge\frac{2006}{4028049}\) khi x=2007

Answer 2

\(A=\frac{1}{2007}-\frac{2}{2007x}+\frac{1}{x^2}=\left(\frac{1}{x^2}-2.\frac{1}{2007}.\frac{1}{x}+\frac{1}{2007^2}\right)+\frac{1}{2007}-\frac{1}{2007^2}.\)

\(=\left(\frac{1}{x}-\frac{1}{2007}\right)^2+\frac{2006}{2007^2}\ge\frac{2006}{2007^2}.\)

\(Amin=\frac{2006}{2007^2}\Leftrightarrow x=2007.\)