Actueel
Archief
Culinair
Didactiek
Documentatie
Etalage
Formules
Fotoboeken
Functies
Geschiedenis
ICT
ICTauteur
Laatste nieuws
Lesmateriaal
Muziek
Natuur
Onderwijs
Ontspanning
Persoonlijk
Probleemaanpak
Proeftuin
Puzzels
Rekenen
Rekenmachines
Ruimtemeetkunde
Schoolwiskunde
Snippers
Systeem
Taal van de wiskunde
Vergelijkingen
Verhalen
WisFaq
WisKast

## Uitwerkingen van de oefeningen

Opgave 1

 $\begin{array}{*{20}c} \begin{array}{l} a. \\ \\ \\ \\ \\ \\ \end{array} & \begin{array}{l} 3x^2 = 5x \\ 3x^2 - 5x = 0 \\ x(3x - 5) = 0 \\ x = 0 \vee 3x - 5 = 0 \\ x = 0 \vee 3x = 5 \\ x = 0 \vee x = 1\frac{2}{3} \\ \end{array} \\ \end{array}$ $\begin{array}{*{20}c} \begin{array}{l} b. \\ \\ \\ \\ \end{array} & \begin{array}{l} (3x + 3)(2x - 5) = 0 \\ 3x + 3 = 0 \vee 2x - 5 = 0 \\ 3x = - 3 \vee 2x = 5 \\ x = - 1 \vee x = 2\frac{1}{2} \\ \end{array} \\ \end{array}$ $\begin{array}{*{20}c} \begin{array}{l} c. \\ \\ \\ \\ \end{array} & \begin{array}{l} (3x - 1)^2 = 16 \\ 3x - 1 = - 4 \vee 3x - 1 = 4 \\ 3x = - 3 \vee 3x = 5 \\ x = - 1 \vee x = 1\frac{2}{3} \\ \end{array} \\ \end{array}$ $\begin{array}{*{20}c} \begin{array}{l} d. \\ \\ \\ \\ \\ \\ \\ \end{array} & \begin{array}{l} (x + 2)^2 + (x + 3)^2 = 1 \\ x^2 + 4x + 4 + x^2 + 6x + 9 = 1 \\ 2x^2 + 10x + 13 = 1 \\ 2x^2 + 10x + 12 = 0 \\ x^2 + 5x + 6 = 0 \\ (x + 2)(x + 3) = 0 \\ x = - 2 \vee x = - 3 \\ \end{array} \\ \end{array}$ $\begin{array}{*{20}c} \begin{array}{l} e. \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \end{array} & \begin{array}{l} 8x^2 + 2x - 3 = 0 \\ 8\left( {x^2 + \frac{1}{4}x} \right) - 3 = 0 \\ 8\left( {\left( {x + \frac{1}{8}} \right)^2 - \frac{1}{{64}}} \right) - 3 = 0 \\ 8\left( {x + \frac{1}{8}} \right)^2 - \frac{1}{8} - 3 = 0 \\ 8\left( {x + \frac{1}{8}} \right)^2 - 3\frac{1}{8} = 0 \\ 8\left( {x + \frac{1}{8}} \right)^2 = 3\frac{1}{8} \\ \left( {x + \frac{1}{8}} \right)^2 = \frac{{25}}{{64}} \\ x + \frac{1}{8} = - \frac{5}{8} \vee x + \frac{1}{8} = \frac{5}{8} \\ x = - \frac{3}{4} \vee x = \frac{1}{2} \\ \end{array} \\ \end{array}$ $\begin{array}{*{20}c} \begin{array}{l} f. \\ \\ \\ \end{array} & \begin{array}{l} 12x^2 = 144 \\ x^2 = 12 \\ x = - \sqrt {12} \vee x = \sqrt {12} \\ \end{array} \\ \end{array}$

Opgave 2

$\begin{array}{l} f(x) = x^2 + 2x - 1 = \left( {x + 1} \right)^2 - 2 \to Top( - 1, - 2) \\ g(x) = - 2x^2 + 6 \to Top(0,6) \\ h(x) = 3x^2 - 30x + 50 = 3(x - 5)^2 - 25 \to Top(5, - 25) \\ k(x) = - 4x^2 - 16x - 28 = - 4(x + 2)^2 - 12 \to Top( - 2, - 12) \\ \end{array}$

Opgave 3

 a. $\begin{array}{l} x^2 + 4x = - 10 \\ (x + 2)^2 - 4 = - 10 \\ (x + 2)^2 = - 6 \\ {\rm{Geen}}\,\,{\rm{oplossing}} \\ \end{array}$ b. $\begin{array}{l} 2\left( {x^2 + 3} \right) = 2 \\ x^2 + 3 = 1 \\ x^2 = - 2 \\ {\rm{Geen}}\,\,{\rm{oplossing}} \\ \end{array}$ c. $\begin{array}{l} 4x^2 - 4x + 1 = 25 \\ 4x^2 - 4x - 24 = 0 \\ x^2 - x - 6 = 0 \\ (x - 3)(x + 2) = 0 \\ x = 3 \vee x = - 2 \\ \end{array}$ d. $\begin{array}{l} (2x + 2)^2 = (3x - 3)^2 \\ 2x + 2 = 3x - 3 \vee 2x + 2 = - 3x + 3 \\ - x = - 5 \vee 5x = 1 \\ x = 5 \vee x = \frac{1}{5} \\ \end{array}$