Question

Bài 1:a) Rút gọn A và B:

\(A=\dfrac{1,11+0,19-1,3.2}{2,06+0,54}-\left(\dfrac{1}{2}+\dfrac{1}{3}\right):2\)

\(B=\left(5\dfrac{7}{8}-2\dfrac{1}{4}-0,5\right):2\dfrac{23}{26}\)

b) Tìm \(x\in Z\) để \(A< x< B\)

Bài 2: Tìm GTNN:

\(M=\left|x-2002\right|+\left|x-2001\right|\)

Answer 1

\(M=\left|x-2002\right|+\left|x-2001\right|\)\(=\left|x-2002\right|+\left|2001-x\right|\ge\left|x-2002+2001-x\right|=\left|-2002+2001\right|=1\)

tức \(M\ge1\) \(\Leftrightarrow\left[{}\begin{matrix}x-2001=0\\x-2002=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2001\\x=2002\end{matrix}\right.\)

Vậy Min_M = - 1 \(\Leftrightarrow\left[{}\begin{matrix}x=2001\\x=2002\end{matrix}\right.\)