`3)`
`a)3(x-2)^2-3x(x+1)=-2`
`⇔3(x^2-4x+4)-3x^2-3x=-2`
`⇔3x^2-12x+12-3x^2-3x=-2`
`⇔3x^2-12x-3x^2-3x=-2-12`
`⇔(3x^2-3x^2)+(-12x-3x)=-14`
`⇔-15x=-14`
`⇔x=(-14)/(-15)`
`⇔x=14/15`
Vậy `x=14/15`
`b)5(x-1)(x+1)-(2x+1)^2=x^2+5x-3`
`⇔5(x^2-1)-[(2x)^2+2.2x.1+1]=x^2+5x-3`
`⇔5x^2-5-(4x^2+4x+1)=x^2+5x-3`
`⇔5x^2-5-4x^2-4x-1=x^2+5x-3`
`⇔5x^2-4x^2-4x-x^2-5x=-3+1+5`
`⇔(5x^2-4x^2-x^2)+(-4x-5x)=3`
`⇔-9x=3`
`⇔x=-3/9`
`⇔x=-1/3`
Vậy `x=-1/3`
`c)(3x-2)(3x+2)-9(x-1)^2=-2x-4`
`⇔[(3x)^2-2^2]-9(x^2-2x+1)=-2x-4`
`⇔(9x^2-4)-9x^2+18x-9=-2x-4`
`⇔9x^2-4-9x^2+18x-9=-2x-4`
`⇔9x^2-9x^2+18x+2x=-4+9+4`
`⇔(9x^2-9x^2)+(18x+2x)=9`
`⇔20x=9`
`⇔x=9/(20)`
Vậy `x=9/(20)`
`d)(5x+1)^2+(2-5x)(5x+2)=4x-3`
`⇔[(5x)^2+2.5x.1+1]+[2^2-(5x)^2]=4x-3`
`⇔25x^2+10x+1+4-25x^2=4x-3`
`⇔25x^2+10x-25x^2-4x=-3-4-1`
`⇔(25x^2-25x^2)+(10x-4x)=-8`
`⇔6x=-8`
`⇔x=-8/6`
`⇔x=-4/3`
Vậy `x=-4/3`
`4)`
`a)x^2-4x+5`
`=x^2-4x+4+1`
`=(x^2-4x+4)+1`
`=(x^2-2.x.2+2^2)+1`
`=(x-2)^2+1`
Ta có:`(x-2)^2≥0∀x`
`⇒(x-2)^2+1≥1∀x`
Vậy `x^2-4x+5_{min}=1` khi `x-2=0⇔x=2`
`b)x^2+6x-7`
`=x^2+6x+9-16`
`=(x^2+6x+9)-16`
`=(x^2+2.x.3+3^2)-16`
`=(x+3)^2-16`
Ta có:`(x+3)^2≥0∀x`
`⇒(x+3)^2-16≥-16∀x`
Vậy `x^2+6x-7_{min}=-16` khi `x+3=0⇔x=-3`
`c)4x^2+6x-7`
`=4(x^2+6/4 .x-7/4)`
`=4(x^2+2.x. 6/8+36/64-37/16)`
`=4(x^2+2.x. 6/8+36/64)-37/4`
`=4[x^2+2.x. 6/8+(6/8)^2]-37/4`
`=4(x+6/8)^2-37/4`
Ta có:`(x+6/8)^2≥0∀x`
`⇒4(x+6/8)^2≥0∀x`
`⇒4(x+6/8)^2-37/4≥-37/4∀x`
Vậy `4x^2+6x-7_{min}=-37/4` khi `x+6/8=0⇔x=-6/8`
`d)9x^2-5x+2`
`=9(x^2-5/9x+2/9)`
`=9(x^2-2.x. 5/(18)+(25)/(324)+(47)/(324))`
`=9(x^2-2.x. 5/(18)+(25)/(324))+(47)/(36)`
`=9[x^2-2.x. 5/(18)+(5/18)^2]+(47)/(36)`
`=9(x-5/(18))^2+(47)/(36)`
Ta có:`(x-5/(18))^2≥0∀x`
`⇒9(x-5/(18))^2≥0∀x`
`⇒9(x-5/(18))^2+(47)/(36)≥(47)/(36)∀x`
Vậy:`9x^2-5x+2_{min}=(47)/(36)` khi `x-5/(18)=0⇔x=5/(18)`
