Giải
a) Ta có: `Q=2x^2 - 6x`
`Q=2.(x^2 - 3x)`
`Q= 2.(x^2 - 2. 3/2 x + 9/4) - 9/2`
`Q=2.(x-3/2)^2 - 9/2`
Vì `(x-3/2)^2 ≥ 0`
`⇒ 2.(x-3/2)^2 ≥ 0 `
`⇒ 2. (x-3/2) - 9/2 ≥ -9/2`
Dấu "=" xảy ra ⇔ `2. (x-3/2) - 9/2 = -9/2`
⇔ `2.(x-3/2) = 0`
⇔ `x-3/2 = 0`
⇔ `x= 3/2`
Vậy `GTNN` của `Q = -9/2` khi `x=3/2`
b) Ta có: `M = x ² + y ² - x + 6y + 10`
`M=(x^2 - x) + (y^2 + 6y + 9) + 1`
`M=(x^2 - 2. 1/2x + 1/4) + (y+3)^2 + 3/4`
`M=(x-1/2)^2 + (y+3)^2 + 3/4`
Vì `(x-1/2)^2 ≥ 0`
`(y+3)^2 ≥ 0`
⇒ `(x-1/2)^2 + (y+3)^2 ≥ 0`
⇒ `(x-1/2)^2 + (y+3)^2 + 3/4 ≥ 3/4`
Dấu "=" xảy ra ⇔ `(x-1/2)^2 + (y+3)^2 = 0`
⇔ $\left \{ {{x-1/2=0} \atop {y+3=0}} \right.$
⇔ $\left \{ {{x=1/2} \atop {y=-3}} \right.$
Vậy ....
c) Ta có: `N = x ² + 5x + 7`
`N=(x^2 + 2. 5/2x + 25/4) + 3/4`
`N = (x+5/2)^2 + 3/4`
Vì `(x+5/2)^2 ≥ 0`
⇒ `(x+5/2)^2 + 3/4 ≥ 3/4`
Dấu "=" xảy ra ⇔ `(x+5/2)^2=0`
`⇔ x+5/2=0`
`⇔ x=-5/2`
Vậy....
