tìm gtnn 15, 3x^2 + 12x + 20 16, 4x^2 - 8x + 30

`15, 3x^2 + 12x + 20`

`=3x^2+12x+12+8`

`=3(x^2+4x+4)+8`

`=3(x^2+2.x.2+2^2)+8`

`=3(x+2)^2+8`

Vì `(x+2)^2>=0`

`=>3(x+2)^2>=0`

`=>3(x+2)^2+8 >=8`

Hay `3x^2 + 12x + 20>=8`

Dấu `=` xảy ra khi:

`3(x+2)^2=0`

`=>(x+2)^2=0`

`=>x+2=0`

`=>x=-2`

Vậy `3x^2 + 12x + 20` có GTNN là `8` khi `x=-2`

`16, 4x^2 - 8x + 30`

`=4x^2-8x+4+26`

`=4(x^2-2x+1)+26`

`=4(x^2-2.x.1+1^2)+26`

`=4(x-1)^2+26`

Vì `(x-1)^2>=0`

`=>4(x-1)^2>=0`

`=>4(x-1)^2+26 >=26`

Hay `4x^2 - 8x + 30>=26`

Dấu `=` xảy ra khi:

`4(x-1)^2=0`

`=>(x-1)^2=0`

`=>x-1=0`

`=>x=1`

Vậy `4x^2 - 8x + 30` có GTNN là `26` khi `x=1`