` A=4x^2+12x+19 `

` =(2x)^2+2.2x.3+3^2+10 `

` =(2x+3)^2+10≥10∀x `

Dấu "=" xảy ra khi: ` (2x+3)^2=0 `

` =>2x+3=0 `

` =>2x=-3=>x=-3/2 `

` => ` $A_{MIN}=10 $ tại ` x=-3/2 `

` B=x^2+6x+1 `

` =x^2+6x+9-8 `

` =x^2+2.x.3+3^2-8 `

` =(x+3)^2-8≥-8∀x `

Dấu "=" xảy ra khi: ` (x+3)^2=0 `

` =>x+3=0=>x=-3 `

` => ` $B_{MIN}=-8 $ tại ` x=- 3 `

` C=9y^2-24x+80 `

` =(3y)^2-2.3y.4+4^2+64 `

` =(3y-4)^2+64≥64∀y `

Dấu "=" xảy ra khi: ` (3y-4)^2=0 `

` =>3y-4=0 `

` =>3y=4=>y=4/3`

` => ` $B_{MIN}=64$ tại ` x=4/3 `

` D=x^2+4y^2+8x-6y+9 `

` =(x^2+8x+16)+(4y^2-6y+9/4)-37/4 `

` =(x^2+2.x.4+4^2)+[(2y)^2-2.2y .3/2+(3/2)^2]-37/4 `

` =(x+4)^2+(2y-3/2)^2-37/4≥-37/4∀x;y `

Dấu "=" xảy ra khi: $\begin{cases}(x+4)^2=0\\(2y-\dfrac{3}{2})^2=0\\\end{cases}$

` => ` $\begin{cases}x+4=0\\2y-\dfrac{3}{2}=0\\\end{cases}$

` => ` $\begin{cases}x=-4\\2y=\dfrac{3}{2}\\\end{cases}$ ` => ` $\begin{cases}x=-4\\y=\dfrac{3}{4}\\\end{cases}$

` => ` $D_{MIN}=-37/4 $ tại ` x=-4;y=3/4 `

` E=x^2+y^2-3x-5y+18 `

` =(x^2-3x+9/4)+(y^2-5y+25/4)+19/2 `

` =[x^2-2.x .3/2+(3/2)^2]+[y^2-2.y .5/2+(5/2)^2]+19/2 `

` =(x-3/2)^2+(y-5/2)^2+19/2≥19/2∀x;y `

Dấu "=" xảy ra khi: $\begin{cases}(x-\dfrac{3}{2})^2=0\\(y-\dfrac{5}{2})^2=0\\\end{cases}$

` => ` $\begin{cases}x-\dfrac{3}{2}=0\\y-\dfrac{5}{2}=0\\\end{cases}$ ` => ` $\begin{cases}x=\dfrac{3}{2}\\y=\dfrac{5}{2}\\\end{cases}$

` => ` $E_{MIN}$ ` =19/2 ` tại ` x=3/2;y=5/2 `