Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Wat is de oplossing van de volgende irrationale vergelijking? $https://latex.codecogs.com/png.image?\inline \dpi{120}\frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}}=3$	A. 0,333...
	B. 0,6
	C. 1,2
	D. 1,8
	E. 2,4

[ 5-8448 - op net sinds 26.5.2019-(E)-3.11.2024 ]

Translation in E N G L I S H

What is de solution of the next equation ? $https://latex.codecogs.com/png.image?\inline \dpi{120}\frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}}=3$	A.
	B. 0.6
	C. 1.2
	D. 1.8
	E. 2.4

Oplossing - Solution

$\frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}}=3\\\sqrt{3+x}+\sqrt{3-x}=3\sqrt{3+x}-3\sqrt{3-x}\\4\sqrt{3-x}=2\sqrt{3+x}\\2\sqrt{3-x}=\sqrt{3+x}\\4(3-x)=3+x\quad(geen\;K.V.)\\12-4x=3+x\\9=5x\\x=\frac95=\frac{18}{10}=1,8$