Question

Bài 1

Tìm GTNN của

B= | 3x - 5 | + | 2 - 3x |

Bài 2

C= | 2x - 20 | - | 2x + 3 |

Trả lời nhanh đi mọi người ơi !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

Bài 1 mình đã làm ở olm rồi: https://olm.vn/hoi-dap/question/1325771.html

Answer 2

Bài 1 :

B=|3x-5|+|2-3x|

\(\Rightarrow B=\left|5-3x\right|+\left|3x-2\right|\\ \Rightarrow B\ge\left|5-3x+3x-2\right|=3\\ \Rightarrow B\ge3\)

Dấu "=" xảy ra

\(\Leftrightarrow\left(5-3x\right).\left(3x-2\right)\ge0\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}5-3x\ge0\\3x-2>0\end{matrix}\right.\\\left\{{}\begin{matrix}5-3x\le0\\3x-2< 0\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3x\le5\\3x>2\end{matrix}\right.\\\left\{{}\begin{matrix}3x\ge5\\3x< 2\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\le\dfrac{5}{3}\\x>\dfrac{2}{3}\end{matrix}\right.\\\left\{{}\begin{matrix}x\ge\dfrac{5}{3}\\x< \dfrac{2}{3}\end{matrix}\right.\end{matrix}\right.\)

Mà \(\left\{{}\begin{matrix}x\ge\dfrac{5}{3}\\x< \dfrac{2}{3}\end{matrix}\right.\) ( vô lí)

\(\Rightarrow\dfrac{2}{3}< x\le\dfrac{5}{3}\)

Vậy \(B_{min}=3\Leftrightarrow\dfrac{2}{3}< x\le\dfrac{5}{3}\)