`\text( Bài 1:)`
`A=x^2+8x`
`=x^2+8x+16-16`
`=x^2+2.4.x+4^2-16`
`=(x+4)^2-16`
Vì `(x+4)^2∀x`
`->(x+4)^2-16>=-16∀x`
`->A>=-16∀x`
Dấu `'='` xảy ra `<=>x+4=0`
`<=>x=-4`
Vậy `A_{min}=-16` khi `x=-4`
`B=x^2+2x+4`
`=x^2+2x+1+3`
`=(x+1)^2+3`
Vì `(x+1)^2≥0∀x`
`->(x+1)^2+3>=3∀x`
`->B>=3∀x`
Dấu `'='` xảy ra `<=>x+1=0`
`<=>x=-1`
Vậy `B_{min}=3` khi `x=-1`
`C=1/4 x^2 +x+3`
`=1/4 x^2 +x +1 +2`
`=(1/2 x)^2 +2 . 1/2 .x +1+2`
`=(1/2 x +1)^2+2`
Vì `(1/2 x +1)^2>=0∀x`
`->(1/2 x+1)^2+2>=2∀x`
`->C>=2∀x`
Dấu `'='` xảy ra `<=>1/2 x+1=0`
`<=>1/2 x=-1<=>x=-2`
Vậy `C_{min}=2` khi `x=-2`
`\text( Bài 2)`
`A=48-y^2-2y`
`=-y^2-2y-1+49`
`=-(y^2+2y+1)+49`
`=-(y+1)^2+49`
Vì `(y+1)^2>=0∀y`
`->-(y+1)^2<=0∀y`
`->-(y+1)^2+49<=49∀y`
`->A≤49∀y`
Dấu `'='` xảy ra `<=>y+1=0`
`<=>y=-1`
Vậy `A_{max}=49` khi `y=-1`
`B=4-x^2+2x`
`=-x^2+2x-1+5`
`=-(x^2-2x+1)+5`
`=-(x-1)^2+5`
Vì `(x-1)^2>=0∀x`
`->-(x-1)^2<=0∀x`
`->-(x-1)^2+5<=5∀x`
`->B<=5∀x`
Dấu `'='` xảy ra `<=>x-1=0`
`<=>x=1`
Vậy `B_{max}=5` khi `x=1`
`C=4x-x^2`
`=-x^2+4x-4+4`
`=-(x^2-4x+4)+4`
`=-(x-2)^2+4`
Vì `(x-2)^2>=0∀x`
`->-(x-2)^2<=0∀x`
`->-(x-2)^2+4<=4∀x`
`->C<=4∀x`
Dấu `'='` xảy ra `<=>x-2=0`
`<=>x=2`
Vậy `C_{max}=4` khi `x=2`
