Đáp án:
`D=-2x^2-2x+5`
`=-2.(x^2+x-5/2)`
`=-2.(x^2+2.(1)/(2).x+(1/2)^2-(1/2)^2-5/2)`
`=-2.[(x+1/2)^2-(11)/(4)]`
`=-2(x+1/2)^2-2.(-11)/(4)`
`=-2(x+1/2)^2+11/2`
Vì `(x+1/2)^2≥0∀x`
`->2.(x+1/2)^2≥0`
`->-2.(x+1/2)^2≤0`
`->-2.(x+1/2)^2+11/2≤11/2`
Dấu bằng xảy ra `⇔(x+1/2)^2=0`
`⇔x+1/2=0`
`⇔x=-1/2`
Vậy `D` đạt GTLN là `11/2` khi `x=-1/2`