Question

Tìm GTNN của:

a. \(A=\left|x+1\right|-2\)

b. \(B=\left|x-1\right|+\left|3-x\right|\)

c. \(C=\left|x-4\right|+\left|3-x\right|\)

Answer 1

\(A=\left|x+1\right|-2\)

\(\left|x+1\right|\ge0\Rightarrow\left|x+1\right|-2\ge-2\)

Dấu "=" xảy ra khi:

\(x=-1\)

\(B=\left|x-1\right|+\left|3-x\right|\)

\(B\ge\left|x-1+3-x\right|\)

\(B\ge2\)

Dấu "=" xảy ra khi:

\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1\ge0\Rightarrow x\ge1\\3-x\ge0\Rightarrow x\le3\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\Rightarrow x< 1\\3-x< 0\Rightarrow x>3\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow1\le x\le3\)

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