Đáp án:
3
`min` `A = -13`
`min` `B = -17/4`
4
`max` `P=85/4`
Giải thích các bước giải:
3
`A = 2x^2-12x+5=(x^2-6x+9)+(x^2-6x+9)-13=(x-3)^2+(x-3)^2-13`
`(x-3)^2≥0` `∀x`
`⇒(x-3)^2+(x-3)^2≥0`
`⇒(x-3)^2+(x-3)^2-13≥-13`
`⇔A≥-13`
`min` `A = -13 ⇔ x-13=0 ⇔x=3`
`B=x^2-5x+2=x^2-2.x.(5)/2+25/4-17/4=(x-2/5)^2-17/4`
`(x-2/5)^2≥0` `∀x`
`⇒(x-2/5)^2-17/4≥-17/4`
`⇔B≥-17/4`
`min` `B = -17/4⇔x-2/5=0⇔x=2/5`
4
`P=9-x^2+7x=-(x^2-7x-9)=-(x^2-2.x.(7)/2+49/4-85/4)=-(x-7/2)^2+85/4`
`(x-7/2)^2≥0` `∀x`
`⇒-(x-7/2)^2≤0`
`⇒-(x-7/2)^2+85/4≤85/4`
`⇔P≤85/4`
`max` `P=85/4⇔x-7/2=0⇔x=7/2`
