A=3(x-4)⁴

Vì (x-4)⁴ ≥0

=>3(x-4)⁴ ≥0

Vậy MinA=0

B=5+2(x-2019)²⁰²⁰

Vì (x-2019)²⁰²⁰ ≥0

=>5+(x-2019)²⁰²⁰ ≥5

Để B đạt Min 

=>x-2019=0

=>x=2019

Vậy MinB=5 <=>x=2019

\(A=\left|4x-3\right|+\left|5y+7,5\right|+17,5\)

Ta thấy \(\left|4x-3\right|\ge0;\left|5y+7,5\right|\ge0\)

\(\Rightarrow\left|4x-3\right|+\left|5y+7,5\right|+17,5\ge17,5\)

\(\Rightarrow A\ge17,5\)

Dấu "=" xảy ra  \(\Leftrightarrow\hept{\begin{cases}4x-3=0\\5y+7,5=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{3}{4}\\y=-1,5\end{cases}}\)

...
\(B=\left|x-2\right|+\left|x-6\right|+2017\)

\(=\left|x-2\right|+\left|6-x\right|+2017\)

Ta thấy \(\left|x-2\right|+\left|6-x\right|\ge\left|x-2+6-x\right|=4\)

\(\Rightarrow B\ge4+2017=2021\)

Dấu "=" xảy ra khi \(2\le x\le6\)

....

\(C=\left(2x+1\right)^{2020}-2019\)

Ta thấy \(\left(2x+1\right)^{2020}\ge0\)

\(\Rightarrow C=\left(2x+1\right)^{2020}-2019\ge-2019\)

Dấu "=" xảy ra khi \(2x+1=0\Leftrightarrow x=-\frac{1}{2}\)

....

Theo bđt cosi 

\(P=\left|x-2019\right|+\dfrac{2020}{\left|x-2019\right|}+2021\ge2\sqrt{\dfrac{\left|x-2019\right|.2020}{\left|x-2019\right|}}+2021=4\sqrt{505}+2021\)

Dấu ''='' xảy ra khi \(x-2019=2020\Leftrightarrow x=4039\)

a, Ta có : \(A=4-\left|2x+5\right|\le4\)

Dấu ''='' xảy ra khi x = -5/2 

Vậy GTLN A là 4 khi x = -5/2 

b, Ta có : \(\left|x-1\right|+5\ge5\)

\(\Rightarrow\dfrac{1}{\left|x-1\right|+5}\le\dfrac{1}{5}\)

Dấu ''='' xảy ra khi x = 1 

Vậy GTLN B là 1/5 khi x = 1

c, \(C=4-\left|x-2\right|-\left|3y+6\right|\le4\)

Dấu ''='' xảy ra khi x = 2 ; y = -2 

Vậy GTLN C là 4 khi x = 2 ; y = -2

a) Ta có: \(\left|2x+5\right|\ge0\forall x\)

\(\Leftrightarrow4-\left|2x+5\right|\le4\forall x\)

Dấu '=' xảy ra khi \(=-\dfrac{5}{2}\)

b) Ta có: \(\left|x-1\right|+5\ge5\forall x\)

\(\Leftrightarrow\dfrac{2019}{\left|x-1\right|+5}\le\dfrac{2019}{5}\forall x\)

Dấu '=' xảy ra khi x=1

c) Ta có: \(-\left|x-2\right|\le0\forall x\)

\(-\left|3y+6\right|\le0\forall y\)

Do đó: \(-\left|x-2\right|-\left|3y+6\right|+4\le4\forall x,y\)

Dấu '=' xảy ra khi x=2 và y=-2