\require{AMSmath}

Uitwerkingen

Opgave 1

1. 6x²+5x-6=0
   a=6, b=5 en c=-6
   D=5²-4·6·-6=25+144=169
   $
   \begin{array}{l}
    x_{1,2}  = \frac{{ - 5 \pm \sqrt {169} }}{{2 \cdot 6}} = \frac{{ - 5 \pm 13}}{{12}} \\
    x = \frac{{ - 5 - 13}}{{12}} \vee \,x = \frac{{ - 5 + 13}}{{12}} \\
    x =  - \frac{{18}}{{12}} \vee x = \frac{8}{{12}} \\
    x =  - 1\frac{1}{2} \vee x = \frac{2}{3}\, \\
    \end{array}
   $
2. 2x²-3x=2
   2x²-3x-2=0
   a=2, b=-3 en c=-2
   D=(-3)²-4·2·-2=9+16=25
   $
   \begin{array}{l}
    x_{1,2}  = \frac{{ -  - 3 \pm \sqrt {25} }}{{2 \cdot 2}} = \frac{{3 \pm 5}}{4} \\
    x = \frac{{ - 2}}{4} \vee x = \frac{8}{4} \\
    x =  - \frac{1}{2} \vee x = 2 \\
    \end{array}
   $
3. 2x²=9x+5
   2x²-9x-5=0
   a=2, b=-9 en c=-5
   D=(-9)²-4·2·-5=81+40=121
   $
   \begin{array}{l}
    x_{1,2}  = \frac{{ -  - 9 \pm \sqrt {121} }}{{2 \cdot 2}} = \frac{{9 \pm 11}}{4} \\
    x = \frac{{ - 2}}{4} \vee x = \frac{{20}}{4} \\
    x =  - \frac{1}{2} \vee x = 5 \\
    \end{array}
   $

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