Wiskundeleraar

Oplossing week 20

Uitwerking

$ \begin{array}{l} \left\{ \begin{array}{l} 2a \cdot 3b = 6912 \\ 8a + 9b = 576 \\ \end{array} \right. \\ \left\{ \begin{array}{l} 6ab = 6912 \\ 8a + 9b = 576 \\ \end{array} \right. \\ \left\{ \begin{array}{l} ab = 1152 \\ 8a + 9b = 576 \\ \end{array} \right. \\ \left\{ \begin{array}{l} a = \frac{{1152}}{b} \\ 8 \cdot \frac{{1152}}{b} + 9b = 576 \\ \end{array} \right. \\ 8 \cdot 1152 + 9b^2 = 576b \\ 8 \cdot 128 + b^2 = 64b \\ b^2 - 64b + 1024 = 0 \\ (b - 32)^2 = 0 \\ \left\{ \begin{array}{l} b = 32 \\ a = 36 \\ \end{array} \right. \\ \end{array} $