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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) (Nếu là tính M khi x = 1)
\(M=\left|1-\frac{1}{2}\right|+\frac{3}{4}=\left|\frac{1}{2}\right|+\frac{3}{4}=\frac{1}{2}+\frac{3}{4}=\frac{5}{4}\)
b) Ta có : \(\left|x-\frac{1}{2}\right|\ge0\)
=> \(\left|x-\frac{1}{2}\right|+\frac{3}{4}\ge\frac{3}{4}\)
GTNN của M là \(\frac{3}{4}\) <=> \(\left|x-\frac{1}{2}\right|=0\) <=> \(x=\frac{1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(M=x-\frac{1}{2}+\frac{3}{4}-x=\left(x-x\right)+\left(\frac{3}{4}-\frac{1}{2}\right)=\frac{1}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1.
b) \(B=\left|x+8\right|+\left|x+18\right|+\left|x+50\right|\)
Ta có:
\(B=\left|x+8\right|+\left|x+18\right|+\left|x+50\right|\ge\left(\left|x+8\right|+\left|-50-x\right|\right)+\left|x+18\right|\)
\(\Rightarrow B=\left(\left|x+8-50-x\right|\right)+\left|x+18\right|\)
\(\Rightarrow B=\left|-42\right|+\left|x+18\right|\)
\(\Rightarrow B=42+\left|x+18\right|\ge42\)
\(\Rightarrow MIN_B=42\) khi và chỉ khi:
\(\left\{{}\begin{matrix}x+8\ge0\\x+18=0\\x+50\ge0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ge-8\\x=-18\\x\ge-50\end{matrix}\right.\Rightarrow x=-18.\)
Vậy \(MIN_B=42\) khi \(x=-18.\)
3.
b) \(\left|x-3\right|-\left|2x+1\right|=0\)
\(\Rightarrow\left|x-3\right|=\left|2x+1\right|\)
\(\Rightarrow\left[{}\begin{matrix}x-3=2x+1\\x-3=-2x-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-2x=1+3\\x+2x=\left(-1\right)+3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}-1x=4\\3x=2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=4:\left(-1\right)\\x=2:3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-4\\x=\frac{2}{3}\end{matrix}\right.\)
Vậy \(x\in\left\{-4;\frac{2}{3}\right\}.\)
Chúc bạn học tốt!
a) Khi x = 1 thì \(M=\left|1-\frac{1}{2}\right|+\frac{3}{4}=\left|\frac{1}{2}\right|+\frac{3}{4}=\frac{1}{2}+\frac{3}{4}=\frac{5}{4}\)
b) Ta có \(\left|x-\frac{1}{2}\right|\ge0\)
\(\Rightarrow\left|x-\frac{1}{2}\right|\) \(+\frac{3}{4}\ge\frac{3}{4}\)
Vậy GTNN của M là \(\frac{3}{4}\) <=> \(\left|x-\frac{1}{2}\right|=0\) <=> x = \(\frac{1}{2}\)