`\text{Đáp án:}`
`A=6`
`B=4`
`C=-29/4`
`D=-33`
`\text{Giải thích các bước giải:}`
`A=x^2+6x+15`
`=(x^2+6x+9)+6`
`=(x+3)^2+6`
`\text{Vì }` `(x+3)^2>=0`
`<=> (x+3)^2+6>=6`
`\text{Dấu "=" xảy ra khi: }` `x+6=0` `<=>x=-6`
`\text{Vậy Min}`$_A$`=6`
`B=9x^2-12x+8`
`=(9x^2-12x+4)+4`
`=(3x+2)^2+4`
`\text{Vì}` `(3x+2)^2>=0`
`<=>(3x+2)^2+4>=4`
`\text{Dấu "=" xảy ra khi:}` `3x+2=0` `<=>x=-2/3`
`\text{Vậy Min}`$_B$ `=4`
`C=16x^2-20x-1`
`=(16x^2-20x+25/4)-29/4`
`=(4x-5/2)^2-29/4`
`\text{Vì}` `((4x-5/2)^2>=0`
`<=>(4x-5/2)^2-29/4 >=-29/4 `
`\text{Dấu "=" xảy ra khi:}` `4x-5/2=0` `<=>` `x=5/8`
`\text{Vậy Min}`$_C$ `=-29/4`
`D=1/4x^2-5x-8`
`=(1/4x^2-5x+25)-33`
`=(1/2x-5)^2-33`
`\text{Vì}` `(1/2x-5)^2>=0`
`<=> (1/2x-5)^2-33>=-33`
`\text{Dấu "=" xảy ra khi:}` `1/2x-5=0` `<=>` `x=10`
`\text{Vậy Min}`$_D$ `=-33`
