`#Sad`
`9)`
`a)`
`x^2-4xy+y^2+2`
`= (x^2-2xy+y^2)-2xy+2`
`= (x-y)^2-2xy+2`
`\text{Vì}` `(x-y)^2 >= 0` `AA x; y in RR`
`⇒ (x-y)^2-2xy+2 > 0` `\text{(→đpcm)}`
`b)`
`x^2-x+1`
`= (x^2-x+1/4)+3/4`
`= (x-1/2)^2+3/4`
`\text{Vì}` `(x-1/2)^2 >= 0` `AA x in RR`
`⇒ (x-1/2)^2+3/4 >= 3/4 > 0` `\text{(→đpcm)}`
`c)`
`x-x^2-2`
`= -x^2+x-2`
`= -(x^2-x+2)`
`= -(x^2-x+1/4)-7/4`
`= -(x-1/2)^2-7/4`
`\text{Vì}` `-(x-1/2)^2 <= 0` `AA x in RR`
`⇒ -(x-1/2)^2-7/4 <= -7/4 < 0` `\text{(→đpcm)}`
