\(\left|x-\frac{1}{2}\right|< \frac{1}{3}\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3\frac{1}{3}\div2\frac{2}{5}-1< x< 7\frac{2}{3}\cdot\frac{3}{7}+\frac{5}{7}\)
\(\frac{25}{18}-1< x< \frac{23}{7}+\frac{5}{7}\)
\(\frac{7}{18}< x< \frac{28}{7}\)
\(\frac{49}{126}< x< \frac{504}{126}\)
\(\Rightarrow x=\left(\frac{50}{126};\frac{51}{126};\frac{52}{126};......;\frac{503}{126}\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(P=\frac{1}{\left(x-2\right)^2}+\frac{1}{\left(3-x\right)^2}+\frac{1}{\left(x-2\right)\left(3-x\right)}\)
\(P\ge\frac{2}{\left(x-2\right)\left(3-x\right)}+\frac{1}{\left(x-2\right)\left(3-x\right)}=\frac{3}{\left(x-2\right)\left(3-x\right)}\)
\(P\ge\frac{3}{\frac{\left(x-2+3-x\right)^2}{4}}=12\)
\(\Rightarrow P_{min}=12\) khi \(x-2=3-x\Rightarrow x=\frac{5}{2}\)
\(\frac{1}{\left(x-2\right)^2}+\frac{1}{\left(x-3\right)^2}\ge\frac{2}{\left(x-2\right)\left(x-3\right)}\)
Bất đẳng thức nào vậy bạn ??
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(-\frac{2}{3}:-\frac{1}{3}\right).\left(-\frac{9}{2}\right)-\frac{1}{4}< \frac{x}{8}< -\frac{1}{2}.\frac{3}{4}:\frac{1}{8}+1\)
\(2.\left(-\frac{9}{2}\right)-\frac{1}{4}< \frac{x}{8}< \left(-3\right)+1\)
\(\left(-9\right)-\frac{1}{4}< \frac{x}{8}< \left(-2\right)\)
\(\left(-\frac{37}{4}\right)< \frac{x}{8}< \left(-2\right)\)
\(-\frac{74}{8}< \frac{x}{8}< -\frac{16}{8}\)
Vậy -74<x<-16
sai đề oy
|x-1/3|<1/2
=>-1/2<x-1/3<1/2
=>-1/2+1/3<x<1/2+1/3
=>-1/6<x<5/6
rùi đó,cô tui chữa lun oy
hok tốt!!