Làm 2 cách cho nó vật vã :
CÁCH 1 :
\(A=\dfrac{x^2-2x+2005}{x^2}=\dfrac{2005\left(x^2-2x+2005\right)}{2005x^2}\)
\(=\dfrac{2005x^2-2x.2005+2005^2}{2005x^2}\)
\(=\dfrac{\left(x^2-2x.2005+2005^2\right)+2004x^2}{2005x^2}\)
\(=\dfrac{\left(x-2005\right)^2}{2005x^2}+\dfrac{2004}{2005}\ge\dfrac{2004}{2005}\)
\(=>Min_A=\dfrac{2004}{2005}\Leftrightarrow x=2005\)
CÁCH 2 :
\(A=\dfrac{x^2-2x+2005}{x^2}\)
\(=1-\dfrac{2}{x}+\dfrac{2005}{x^2}\)
\(=2005\left(\dfrac{1}{x^2}-\dfrac{2}{2005x}\right)+1\)
\(=2005\left(\dfrac{1}{x}-\dfrac{1}{2005}\right)^2+\dfrac{2004}{2005}\ge\dfrac{2004}{2005}\)
\(=>Min_A=\dfrac{2004}{2005}\Leftrightarrow x=2005\)
