Giải phương trình: ` |3x - 2| = x^2 + 2x + 3`

    `|3x-2|=x^2+2x+3`

`@TH1:` `3x-2 >= 0⇔x >= 2/3` 

    `⇒|3x-2|=3x-2`

 Ta có: `3x-2=x^2+2x+3`

       `⇔x^2+2x-3x+3+2=0`

       `⇔x^2-x+5=0`

       `⇔x^2-2x.1/2+1/4+19/4=0`

       `⇔(x-1/2)^2=-19/4` (Vô lí)sqr

`@TH2:` `3x-2 < 0⇔x < 2/3`

  `⇒|3x-2|=2-3x`

Ta có: `2-3x=x^2+2x+3`

     `⇔x^2+2x+3x+3-2=0`

     `⇔x^2+5x+1=0`

     `⇔x^2+2.x.5/2+25/4-21/4=0`

     `⇔(x+5/2)^2=21/4`

      ⇔\(\left[ \begin{array}{l}x+5/2=\frac{\sqrt{21}}{2}\\x+5/2=\frac{-\sqrt{21}}{2}\end{array} \right.\)

      ⇔\(\left[ \begin{array}{l}x=\frac{-5+\sqrt{21}}{2}\\x+5/2=\frac{-5-\sqrt{21}}{2}\end{array} \right.\)

        Mà `x < 2/3`

  ⇒`x=(-5+-\sqrt{21})/2`

Vậy ptr đã cho có nghiệm `x=(-5+-\sqrt{21})/2` 

`|3x-2|=x^2+2x+3`

`@` Trường hợp `1:`

Với `x>=2/3`

`3x-2=x^2+2x+3`

`<=>3x-2-x^2-2x-3=0`

`<=>x^2-(3x-2x)+(-2-3)=0`

`<=>x^2-x+5=0`

`<=>x^2-2x . 1/2+1/5+19/4=0`

`<=>(x-1/2)^2+19/4`

Do `(x-1/2)^2>=0 AA x`

`->(x-1/2)^2+19/4>=19/4>0 AA x`

Nên `(x-1/2)^2\ne19/4`

`->` Vô nghiệm

`@` Trường hợp `2:`

Với `x<2/3`

`3x-2=(-x^2+2x+3)`

`<=>3x-2=-x^2-2x-3`

`<=>3x-2+x^2+2x+3=0`

`<=>x^2+(3x+2x)+(-2+3)=0`

`<=>x^2+5x+1=0`

`<=>x^2+2x . 5/2+25/4-21/4=0`

`<=>(x+5/2)^2-21/4=0`

`<=>(x+5/2)^2=21/4`

`<=>(x+5/2)^2=((\sqrt{21})/2)^2`

`<=>x+5/2=+-(\sqrt{21})/2`

`<=>x+5/2=(\sqrt{21})/2` hoặc `x+5/2=-(\sqrt{21})/2`

`<=>x=(-5+\sqrt{21})/2` hoặc `x=(-5-\sqrt{21})/2`

Mà `x<2/3`

Vậy, `S={(-5+\sqrt{21})/2; (-5-\sqrt{21})/2}.`