Đáp án:
a)
`x^2-3x+5=x^2 - 2 . x . 3/2 + (3/2)^2 + 5 - (3/2)^2`
`= (x-3/2)^2 + 11/4`
Vì : ` (x-3/2)^2 >=0 ∀x`
`\to (x-3/2)^2+11/4>=11/4>0` (đpcm)
b)
`x-x^2-2=-(x^2-x+2)`
`=- [ x^2 - 2 . x . 1/2 + (1/2)^2 + 2 - (1/2)^2]`
`=- [ (x-1/2)^2 +7/4 ]`
`= -(x-1/2)^2 - 7/4`
Vì : `(x-1/2)^2 >=0 ∀x \to -(x-1/2)^2<=0 ∀x`
`to -(x-1/2)^2-7/4<=7/4 <0` (đpcm)