Đáp án:
`B=-x^2-6x+20`
`=-x^2-6x-9+9+20`
`=-(x^2+6x+9)+29`
`=-(x^2+2.3.x+3^2)+29`
`=-(x+3)^2+29`
Vì `(x+3)^2>=0∀x`
`->-(x+3)^2<=0∀x`
`->-(x+3)^2+29<=29∀x`
`->B<=29∀x`
Dấu `=` xảy ra `<=>x+3=0`
`<=>x=-3`
Vậy `B_{max}=29` khi `x=-3`
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`C=-2x^2+5x+21`
`=-2x^2+5x-25/8+25/8+21`
`=-(2x^2-5x+25/8)+193/8`
`=-2(x^2-5/2x +25/16)+193/8`
`=-2.[x^2-2 . 5/4 .x+(5/4)^2]+193/8`
`=-2(x-5/4)^2+193/8`
Vì `(x-5/4)^2>=0∀x`
`->-2(x-5/4)^2<=0∀x`
`->-2(x-5/4)^2+193/8<=193/8∀x`
`->C<=193/8∀x`
Dấu `'='` xảy ra `<=>x-5/4=0`
`<=>x=5/4`
Vậy `C_{max}=193/8` khi `x=5/4`