Giải thích các bước giải :
`C=-(x-2)^2-(2x-1)^2`
`<=>C=-(x^2-4x+4)-(4x^2-4x+1)`
`<=>C=-x^2+4x-4-4x^2+4x-1`
`<=>C=-5x^2+8x-5`
`<=>C=-5(x^2-(8x)/5+1)`
`<=>C=-5[x^2-2×x×4/5+(4/5)^2-(16)/(25)+(25)/(25)]`
`<=>C=-5[x^2-2×x×4/5+(4/5)^2]-5×(25-16)/(25)`
`<=>C=-5(x-4/5)^2-9/5 ≤ -9/5`
Xảy ra dấu `=` khi :
`-5(x-4/5)^2=0 <=> x-4/5=0 <=> x=4/5`
Vậy `C_(max)=-9/5` khi `x=4/5`
`D=2+5x-x^2`
`<=>D=-(x^2-5x-2)`
`<=>D=-[x^2-2×x×5/2+(5/2)^2-(25)/4-8/4]`
`<=>D=-[x^2-2×x×5/2+(5/2)^2]+(25+8)/4`
`<=>D=-(x-5/2)^2+(33)/4 ≤ (33)/4`
Xảy ra dấu `=` khi :
`-(x-5/2)^2=0<=>x-5/2=0<=>x=5/2`
Vậy `D_(max)=(33)/4` khi `x=5/2`
