Đáp án:
`maxA=7`
`maxB=1/4`
`maxC=-9/2`
`maxD=5/4`
Giải thích các bước giải:
`A=4x-x^2+3`
`A=-(x^2-4x-3)`
`A=-(x^2-2.x.2+2^2-7)`
`A=-(x-2)^2+7<=7`
Dấu `=` xảy ra
`<=>x-2=0`
`<=>x=2`
Vậy `maxA=7` khi `x=2`
`B=x-x^2`
`B=-(x^2-x)`
`B=-[x^2-2.x.(1)/2+(1/2)^2-1/4]`
`B=-(x-1/2)^2+1/4<=1/4`
Dấu `=` xảy ra
`<=>x-1/2=0`
`<=>x=1/2`
Vậy `maxB=1/4` khi `x=1/2`
`C=2x-2x^2-5`
`C=-(2x^2-2x+5)`
`C=-2(x^2-x+5/2)`
`C=-2[x^2-2.x.(1)/2+(1/2)^2+9/4]`
`C=-2(x-1/2)^2-9/2<=-9/2`
Dấu `=` xảy ra
`<=>x-1/2=0`
`<=>x=1/2`
Vậy `maxC=-9/2` khi `x=1/2`
`D=-x^2-2y^2+2xy-y+1`
`D=-x^2-y^2-y^2+2xy-y+1`
`D=-(x^2-2xy+y^2)-(y^2+y-1)`
`D=-(x-y)^2-[y^2+2.y.(1)/2+(1/2)^2-5/4]`
`D=-(x-y)^2-(y+1/2)^2+5/4<=5/4`
Dấu `=` xảy ra
`<=>{(x-y=0),(y+1/2=0):}`
`<=>{(x=y),(y=-1/2):}`
`<=>x=y=-1/2`
Vậy `maxD=5/4` khi `x=y=-1/2`
