Đáp án:
`1, M=-2x^2+5x+2`
`M=-2(x^2-5/2x-1)`
`M=-2(x^2-3.x.(5/4)+25/16-41/16)`
`M=41/8-2(x-5/4)^2<=41/8`
dấu = có khi `x-5/4=0<=>x=5/4`
vậy `max M=41/8` khi `x=5/4`
`2, N=(1-2x)(x+3)-9`
`N=x+3-2x^2-6x-9`
`N=-2x^2-5x-6`
`N=-2(x^2+5/2x+3)`
`N=-2(x^2+2.x.(5/4)+25/16+23/16)`
`N=-23/8-2(x+5/4)^2<=-23/8`
dấu = có khi `x+5/4=0<=>x=-5/4`
vậy `max N=-23/8` khi `x=-5/4`