Đáp án:
`GTLN{-1/(x-2)*(x^2-5x+3)*(x-2)}=13/4<=>x=5/2.`
Giải thích các bước giải:
`-1/(x-2)*(x^2-5x+3)*(x-2)(x \ne 2)`
`=(-(x-2)(x^2-5x+3))/(x-2)`
`=-(x^2-5x+3)`
`=-(x^2-2*x*5/2+25/4+3-25/4)`
`=-[(x-5/2)^2-13/4]`
Vì `(x-5/2)^2>=0`
`=>(x-5/2)^2-13/4>=-13/4`
`=>-[(x-5/2)^2-13/4]<=13/4`
Hay `-1/(x-2)*(x^2-5x+3)*(x-2)<=13/4`
Dấu "=" xảy ra khi `x-5/2=0<=>x=5/2`
Vậy `GTLN{-1/(x-2)*(x^2-5x+3)*(x-2)}=13/4<=>x=5/2.`
