1. Tìm GTNN các biểu thức a) A = 4x^2 + 4x + 11 b) C = x^2 – 2x + y^2 – 4y + 7 2. Tìm GTLN a) A= 5 – 8x – x^2 b) B= 5 – x^2 + 2x – 4y^2 – 4y

`1,`

`a) A=4x^2+4x+11`

`A=(4x^2+4x+1)+10`

`A=(2x+1)^2+10>=10`

Dấu = xảy ra khi `2x+1=0<=>x=-1/2`

Vậy `minA=10` khi `x=-1/2`

`b) C=x^2-2x+y^2-4y+7`

`C=(x^2-2x+1)+(y^2-4y+4)+2`

`C=(x-1)^2+(y-2)^2+2>=2`

Dấu = xảy ra khi `x-1=0; y-2=0<=>x=1;y=2`

Vậy `min C=2` khi `x=1; y=2`

`2,`

`a) A=5-8x-x^2`

`A=-(x^2+8x-5)`

`A=-(x^2+8x+16-21)`

`A=21-(x+4)^2<=21`

Dấu =xảy ra khi `x+4=0<=>x=-4`

Vậy `maxA=21` khi `x=-4`

`b) B=5-x^2+2x-4y^2-4y`

`B=-(x^2-2x+4y^2+4y-5)`

`B=-[(x^2-2x+1)+(4y^2+4y+1)-7]`

`B=7-[(x-1)^2+(2y+1)^2]<=7`

Dấu = xảy ra khi `x-1=0; 2y+1=0 <=>x=1; y=-1/2`

Vậy `maxB=7` khi `x=1; y=-1/2`