` 2x^2+2x+1`
`=2.(x^2+x+1/2)`
`=2.(x^2+2x. 1/2 + 1/4 - 1/4+1/2)`
 `=2.[(x^2+2x. 1/2 + 1/4)+1/4]`
`=2.[(x+1/2)^2+1/4].`
Có: `(x+1/2)^2\ge0⇒(x+1/2)^2+1/4\ge1/4>0⇒2.[(x+1/2)^2+1/4]>0`
Vậy` 2x^2+2x+1>0∀x.`
`-x^2+6x-10`
`=-(x^2-6x+10)`
`=-(x^2-6x+9+1)`
`=-[(x^2-6x+9)+1]`
`=-[(x-3)^2+1].`
Có: `(x-3)^2\ge0⇒(x-3)^2+1\ge1>0⇒-[(x-3)^2+1]<0.`
Vậy`-x^2+6x-10<0∀x.`