`1)`
`A=x²-14x+1049`
`=x²-14x+49+1000`
`=(x²-14x+49)+1000`
`=(x²-2.x.7+7²)+1000`
`=(x-7)²+1000`
Ta có:`(x-7)²≥0∀x`
`⇒(x-7)²+1000≥1000∀x`
Vậy `A_(min)=1000` khi `x-7=0⇔x=7`
`B=x²-3x-9`
`=x²-3x+9/4-45/4`
`=(x²-3x+9/4)-45/4`
`=[x²-2.x. 3/2+(3/2)^2]-45/4`
`=(x-3/2)^2-45/4`
Ta có:`(x-3/2)^2≥0∀x`
`⇒(x-3/2)^2-45/4≥-45/4∀x`
Vậy `B_(min)=-45/4` khi `x-3/2=0⇔x=3/2`
`C=4x²-x`
`=4x²-x+1/16-1/16`
`=(4x²-x+1/16)-1/16`
`=[(2x)²-2.2x. 1/4+(1/4)^2]-1/16`
`=(2x-1/4)^2-1/16`
Ta có:`(2x-1/4)^2≥0∀x`
`⇒(2x-1/4)^2-1/16≥-1/16∀x`
Vậy `C_(min)=-1/16` khi `2x-1/4=0⇔x=1/8`
`2)`
`M=18-8x-x²`
`=-(x²+8x-18)`
`=-(x²+8x+16-34)`
`=-(x²+8x+16)+34`
`=-(x²+2.x.4+4²)+34`
`=-(x+4)²+34`
Ta có:`(x+4)²≥0∀x`
`⇒-(x+4)²≤0∀x`
`⇒-(x+4)²+34≤34∀x`
Vậy `M_(max)=34` khi `x+4=0⇔x=-4`
`N=-7-3x-x²`
`=-(x²+3x+7)`
`=-(x²+3x+9/4+19/4)`
`=-(x²+3x+9/4)-19/4`
`=-[x²+2.x. 3/2+(3/2)^2]-19/4`
`=-(x+3/2)^2-19/4`
Ta có:`(x+3/2)^2≥0∀x`
`⇒-(x+3/2)^2≤0∀x`
`⇒-(x+3/2)^2-19/4≤-19/4∀x`
Vậy `N_(max)=-19/4` khi `x+3/2=0⇔x=-3/2`
`P=120-30x-9x²`
`=-(9x²+30x-120)`
`=-(9x²+30x+25-145)`
`=-(9x²+30x+25)+145`
`=-[(3x)²+2.3x.5+5²]+145`
`=-(3x+5)²+145`
Ta có:`(3x+5)²≥0∀x`
`⇒-(3x+5)²≤0∀x`
`⇒-(3x+5)²+145≤145∀x`
Vậy `P_(max)=145` khi `3x+5=0⇔x=-5/3`
