Question

Ai biết làm bài này không ạ?

(x-\(\frac{1}{2}\)).(\(\frac{5}{2}\)+x)<0 (tìm x)

Tìm giá trị nhỏ nhất của:

a)A=3+|2-x|

b)B=|2x+1|-\(\frac{3}{4}\)

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Answer 1

Có!

\(-\frac{1}{2}< x< \frac{5}{2}\)

a) MinA= 3 ⇔ x=2

b) MinB= \(-\frac{3}{4}\) ⇔ x=\(-\frac{1}{2}\)

Answer 2

Tìm x :

\(\left(x-\frac{1}{2}\right).\left(\frac{5}{2}+x\right)< 0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-\frac{1}{2}>0\\\frac{5}{2}+x< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x-\frac{1}{2}< 0\\\frac{5}{2}+x>0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>\frac{1}{2}\\x< -\frac{5}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}x< \frac{1}{2}\\x>-\frac{5}{2}\end{matrix}\right.\end{matrix}\right.\)

Answer 3

a)\(A=3+\left|2-x\right|\Leftrightarrow A=\left|2-x\right|+3\\ Co:\left|2-x\right|\ge0voi\forall x\\ \Rightarrow\left|2-x\right|+3\ge3\\ \Leftrightarrow A\ge3\)

Dấu "=" xảy ra khi \(\left|2-x\right|=0\Rightarrow x=2\)

Vậy A​_min\(=3khi\)\(x=2\)

Answer 4

b)\(B=\left|2x+1\right|-\frac{3}{4}\Leftrightarrow B=\left|2x+1\right|+\left(-\frac{3}{4}\right)\\ Co:\left|2x+1\right|\ge0voi\forall x\\ \Rightarrow\left|2x+1\right|+\left(-\frac{3}{4}\right)\ge\left(-\frac{3}{4}\right)\\ \Leftrightarrow B\ge\left(-\frac{3}{4}\right)\)

Dấu "=" xảy ra khi \(\left|2x+1\right|=0\Rightarrow x=\frac{-1}{2}\)

Vậy B​​_min \(=\frac{-3}{4}khix=\frac{-1}{2}\)