Bài 10:
`1)`
`x^2+2-(x+3)(x+1)=-2`
`⇔x^2+2-(x^2+4x+3)=-2`
`⇔x^2+2-x^2-4x-3=-2`
`⇔-4x-1=-2`
`⇔-4x=-1`
`⇔x=1/4`
Vậy `x=1/4`
`3)`
`(2x-3)(x+2)-(4x-2)(x-5)=-16`
`⇔(2x^2+x-6)-(4x^2-11x+10)=-16`
`⇔2x^2+x-6-4x^2+11x-10=-16`
`⇔-2x^2+12x-16=-16`
`⇔-2x^2+12x=0`
`⇔-2x(x-6)=0`
\(⇔\left[ \begin{array}{l}2x=0\\x-6=0\end{array} \right.\)
\(⇔\left[ \begin{array}{l}x=0\\x=6\end{array} \right.\)
Vậy `x∈\{0;6\}`
`5)`
`5(x-3)+(x-2)(5x-1)=5x^2`
`⇔5x-15+5x^2-11x+2=5x^2`
`⇔-6x-13+5x^2=5x^2`
`⇔-6x-13=0`
`⇔-6x=13`
`⇔x=-13/6`
Vậy `x=-13/6`
`7)`
`(3x-1)(x+2)-(2-3x)(x+2)=12`
`⇔3x^2+5x-2-(-3x^2-4x+4)=12`
`⇔3x^2+5x-2+3x^2+4x-4=12`
`⇔6x^2+9x-6=12`
`⇔6x^2+9x-18=0`
`⇔6.(x^2+3/2x-3)=0`
`⇔x^2+3/2x-3=0`
`⇔x^2+2.x.(3)/4+9/16-57/16=0`
`⇔(x+3/4)^2-(\sqrt57/4)^2=0`
`⇔(x+3/4)^2=(\sqrt57/4)^2`
`⇔x+3/4=±\sqrt57/4`
`⇔x=(-3±\sqrt57)/4`
Vậy `x=(-3±\sqrt57)/4`
Bài 11:
`1)`
`(2x+1)(x-2)-x(2x+3)+10`
`=2x^2-4x+x-2-2x^2-3x+10`
`=2x^2-3x-2-2x^2-3x+10`
`=-6x+8`
`3)`
`-3(x+1)(2x+3)+9x^2+3(5x+6)`
`=-3(2x^2+3x+2x+3)+9x^2+15x+18`
`=-3(2x^2+5x+3)+9x^2+15x+18`
`=-6x^2-15x-9+9x^2+15x+18`
`=(-6x^2+9x^2)+(-15x+15x)+(-9+18)`
`=3x^2+9`
