a)Ta thấy:

\(\left(2x+\frac{1}{3}\right)^2\ge0\)

\(\Rightarrow\left(2x+\frac{1}{3}\right)^2-\frac{5}{6}\ge0-\frac{5}{6}=-\frac{5}{6}\)

\(\Rightarrow A\ge-\frac{5}{6}\)

Dấu "=" <=>x=-1/6

Vậy MinA=-5/6<=>x=-1/6

b)Ta thấy:\(\hept{\begin{cases}\left|2x+3\right|\\\left|y-\frac{1}{2}\right|\end{cases}\ge}0\)

\(\Rightarrow\left|2x-3\right|+\left|y-\frac{1}{2}\right|\ge0\)

\(\Rightarrow\left|2x-3\right|+\left|y-\frac{1}{2}\right|+\frac{3}{4}\ge0+\frac{3}{4}=\frac{3}{4}\)

\(\Rightarrow B\ge\frac{3}{4}\)

Dấu "=" xảy ra khi \(\hept{\begin{cases}\left|2x-3\right|=0\\\left|y-\frac{1}{2}\right|=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{3}{2}\\y=\frac{1}{2}\end{cases}}\)

Vậy...

\(\text{a)Để C đạt GTNN}\)

\(\Rightarrow\hept{\begin{cases}\left(x+2\right)^2\\\left(y-\frac{1}{5}\right)^2\end{cases}\ge0}\)

\(\Rightarrow\left(x+2\right)^2+\left(y-\frac{1}{5}\right)^2\ge0\)

\(\Rightarrow\left(x+2\right)^2+\left(y-\frac{1}{5}\right)^2-10\ge0-10\)

\(\Rightarrow C\ge-10\)

\(\text{Vậy minC=-10 khi x=-2;y= }\frac{1}{5}\)

b)\(\text{Để D đạt GTLN}\)

=>(2x-3)²+5 đạt GTNN

Mà (2x-3)²\(\ge\)5

\(\Rightarrow GTLN\)của \(A=\frac{4}{5}\)khi \(x=\frac{3}{2}\)

a ) \(A=\left|2x-2\right|+\left|2x-2019\right|\ge\left|2-2x+2x-2019\right|=\left|2-2019\right|=2017\)

Để A đạt GTNN là 2017 <=> \(\left(2-2x\right)\left(2x-2019\right)\ge0\Rightarrow1\le x\le\frac{2019}{2}\)

b ) \(\left|2x-4\right|-\left|6-3x\right|=-1\)

\(\Leftrightarrow2\left|x-2\right|-3\left|x-2\right|=-1\)

\(\Leftrightarrow-\left|x-2\right|=-1\)

\(\Rightarrow\left|x-2\right|=1\)

\(\Rightarrow x=1;3\)

Mà x lớn nhất => x = 3

\(\left|x-1\right|+2C=\left|x-1,5\right|+\left|1-x\right|\\ \Leftrightarrow\left|x-1\right|+2C=\left|x-1,5\right|+\left|x-1\right|\\ \Rightarrow2C=\left|x-1,5\right|\ge0\\ \Rightarrow C\ge0\)

Để C=0 thì

\(\left|x-1,5\right|=0\\ \Leftrightarrow x-1,5=0\\ \Leftrightarrow x=1,5\)

Vậy...

cái này sai r mk xóa nhé

Đề full ko phải vệ,có lẽ bạn đó viết quá gần

\(A=\left|2x-1\right|+\left|2x-2019\right|=\left|2x-1\right|+\left|2019-2x\right|\)

\(\ge\left|2x-2x-1+2019\right|=2018\)

Dấu "=" xảy ra \(\Leftrightarrow\left(2x-1\right)\left(2019-2x\right)\ge0\).Tự giải tiếp.

Lam giup minh voi

|2x-7| >= 0

=>|2x-7|+5-2x >= 5-2x

=>A_Min=5-2x(*)

dấu "=" xảy ra<=>|2x-7|=0<=>x=7/2

thay x=7/2 vào (*) ta có:

A_Min=5-2.7/2=-2

Vậy A_Min=-2 tại x=7/2

|2x-7| >= 0

=>|2x-7|+5-2x >= 5-2x

=>A_Min=5-2x(*)

dấu "=" xảy ra<=>|2x-7|=0<=>x=7/2

thay x=7/2 vào (*) ta có:

A_Min=5-2.7/2=-2

Vậy A_Min=-2 tại x=7/2