Question

tim gia tri nho nhat cua bieu thuc:

A=lx-2001l + lx-1l

Answer 1

\(A=\left|x-2001\right|+\left|x-1\right|\)

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

Áp dụng Bđt \(\left|a\right|+\left|b\right|\ge\left|a+b\right|\) ta có:

\(\left|x-2001\right|+\left|1-x\right|\ge\left|x-2001+1-x\right|=2000\)

\(\Rightarrow A\ge2000\)

Dấu = khi \(\begin{cases}x-2001\le0\\x-1\ge0\end{cases}\)\(\Rightarrow\begin{cases}x\le2001\\x\ge1\end{cases}\)\(\Rightarrow1\le x\le2001\)

Vậy Min_A=2000 khi \(1\le x\le2001\)