Question

Câu1. Tìm giá trị nhỏ nhất

A=|x-2018|+|2019+x|              B=x(x-2)+2(x-3/2)

Giúp mk rồi mk sẽ tick cho.nhớ làm đầy đủ giùm mk

Answer 1

\(A=\left|x-2018\right|+\left|x+2019\right|\)

\(A=\left|2018-x\right|+\left|x+2019\right|\)

\(A\ge\left|2018-x+x+2019\right|=\left|4037\right|=4037\)

Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}2018-x\ge0\\x+2019\ge0\end{cases}\Leftrightarrow\hept{\begin{cases}x\le2018\\x\ge-2019\end{cases}\Leftrightarrow}-2019\le x\le2018}\)

Vậy.........

Answer 2

\(1,A=\left|x-2018\right|+\left|2019+x\right|\)

\(\Rightarrow A\ge\left|x-2018-\left(2019+x\right)\right|\)

\(\Rightarrow A\ge\left|x-2018-2019-x\right|\)

\(\Rightarrow A\ge\left|-2018-2019\right|\)

\(\Rightarrow A\ge\left|-4037\right|=4037\)

Vậy \(A_{min}=4037\)