Đáp án:
$\rm \text{Áp dụng BĐT:}|A|+|B| \geq |A+B|\\\to \begin{cases}|x-2004|+|x-2007|=|x-2004|+|2007-x| \geq |x-2004+2007-x|=3\\|x-2005|+|x-2006|=|x-2005|+|2006-x| \geq |x-2005+2006-x|=1\end{cases}\\\to A \geq 3+1=4\\\text{Dấu "=" xảy ra khi:}\\\begin{cases}(x-2004)(2007-x) \geq 0\\(x-2005)(x-2006) \geq 0\end{cases}\\↔\begin{cases}(x-2004)(x-2007) \leq 0\\(x-2005)(x-2006) \leq 0\end{cases}\\↔\begin{cases}2004 \leq x \leq 2007\\2005 \leq x \leq 2006\end{cases}\\↔2005 \leq x \leq 2006$
