Đáp án+Giải thích các bước giải:
`B=-x^2+2x-8`
`=-x^2+2x-1-7`
`=-(x^2-2x+1)-7`
`=-(x^2-2.x.1+1^2)-7`
`=-(x-1)^2-7`
Vì `(x-1)^2≥0` `=>-(x-1)^2≤0`
`=>-(x-1)^2-7≤-7`
Dấu "`=`" xảy ra khi:
`-(x-1)^2=0`
`=>x-1=0`
`=>x=1`
Vậy `min` `B=-7` khi `x=1`
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`E=-25x^2-10x+30`
`=-25x^2-10x-1+31`
`=-(25x^2+10x+1)+31`
`=-[(5x)^2+2.5x.1+1^2]+31`
`=-(5x+1)^2+31`
Vì `(5x+1)^2≥0` `=>-(5x+1)^2≤0`
`=>-(5x+1)^2≤31`
Dấu "`=`" xảy ra khi:
`-(5x+1)^2=0`
`=>5x+1=0`
`=>5x=-1`
`=>x=-1/5`
Vậy `min` `E=31` khi `x=-1/5`
-------------------------------------------------
`F=-3x^2+6x-42`
`=-3x^2+6x-3-39`
`=-(3x^2-6x+3)-39`
`=-[(\sqrt{3}x)^2-2.\sqrt{3}x.\sqrt{3}+(\sqrt{3})^2]-39`
`=-(\sqrt{3}x-\sqrt{3})^2-39`
Vì `(\sqrt{3}x-\sqrt{3})^2≥0`
`=>-(\sqrt{3}x-\sqrt{3})^2≤0`
`=>-(\sqrt{3}x-\sqrt{3})^2-39≤-39`
Dấu "`=`" xảy ra khi:
`-(\sqrt{3}x-\sqrt{3})^2=0`
`=>\sqrt{3}x-\sqrt{3}=0`
`=>\sqrt{3}x=\sqrt{3}`
`=>x=\sqrt{3}:\sqrt{3}`
`=>x=1`
Vậy `min` `F=-39` khi `x=1`
