Đáp án :
`+)P_(min)=-2` khi `x=0`
`+)P_(max)=2` khi `x=-2`
Giải thích các bước làm :
`+)P=(x^2-2x-2)/(x^2+x+1) (tm∀x)`
`=>P+2=(x^2-2x-2)/(x^2+x+1)+2`
`=>P+2=(x^2-2x-2)/(x^2+x+1)+(2(x^2+x+1))/(x^2+x+1)`
`=>P+2=(x^2-2x-2)/(x^2+x+1)+(2x^2+2x+2)/(x^2+x+1)`
`=>P+2=(x^2-2x-2+2x^2+2x+2)/(x^2+x+1)`
`=>P+2=(3x^2)/(x^2+x+1)>=0`
`=>P+2>=0`
`=>P>=-2`
`=>P_(min)=-2`
Xảy ra dấu "=" khi :
`(3x^2)/(x^2+x+1)=0`
`=>3x^2=0`
`=>x^2=0`
`=>x=0`
`+)P=(x^2-2x-2)/(x^2+x+1)`
`=>P-2=(x^2-2x-2)/(x^2+x+1)-2`
`=>P-2=(x^2-2x-2)/(x^2+x+1)-(2(x^2+x+1))/(x^2+x+1)`
`=>P-2=(x^2-2x-2)/(x^2+x+1)-(2x^2+2x+2)/(x^2+x+1)`
`=>P-2=(x^2-2x-2-2x^2-2x-2)/(x^2+x+1)`
`=>P-2=(-x^2-4x-4)/(x^2+x+1)`
`=>P-2=(-(x^2+4x+4))/(x^2+x+1)`
`=>P-2=(-(x+2)^2)/(x^2+x+1)<=0`
`=>P-2<=0`
`=>P<=2`
`=>P_(max)=2`
Xảy ra dấu "=" khi :
`(-(x+2)^2)/(x^2+x+1)=0`
`=>(x+2)^2=0`
`=>x+2=0`
`=>x=-2`
Vậy :
`+)P_(min)=-2` khi `x=0`
`+)P_(max)=2` khi `x=-2`