`\text{Đáp án:}`
`1)` `1/4`
`2)` `-9/2`
`\text{Giải thích các bước giải:}`
`1)` `A=x-x^2`
`=-(x^2-2*x*1/2+1/4)+1/4`
`=-(x-1/2)^2+1/4`
`\text{Vì}` `-(x-1/2)^2 \le 0`
`\text{Nên}` `-(x-1/2)^2+1/4\le 1/4`
`\text{Dấu "=" xảy ra khi:}` `x-1/2=0⇔x=1/2`
`\text{Vậy}` `Max_A` `=1/4` `\text{khi}` `x=1/2`
`2)` `B=2x-2x^2-5`
`=-2[(x^2-2*x*1/2+1/4)+9/4]`
`=-2[(x-1/2)^2+9/4]`
`=-2(x-1/2)^2-9/2`
`\text{Vì}` `-(x-1/2)^2 \le0`
`\text{Nên}` `-2(x-1/2)^2 \le 0`
`⇒-2(x-1/2)^2-9/2 \le -9/2`
`\text{Dấu "=" xảy ra khi:}` `x-1/2=0⇔x=1/2`
`\text{Vậy}` `Max_B` `=-9/2` `\text{khi}` `x=1/2`
