Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Wat is de oplossing van de vergelijking $\sqrt 5\: x = \sqrt 4 + \sqrt 3\: x$	A. 1
	B. 2
	C.
	D.
	E. +

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Translation in E N G L I S H

What is the solution of the equation $\sqrt 5\: x = \sqrt 4 + \sqrt 3\: x$	A. 1
	B. 2
	C.
	D.
	E. +

Oplossing - Solution

$\begin{aligned} & \sqrt 5\: x = \sqrt 4 + \sqrt 3\: x\\ & \Leftrightarrow \sqrt 5\: x-\sqrt 3\: x=2\\ & \Leftrightarrow (\sqrt 5-\sqrt3)x=2\\ & \Leftrightarrow x=\frac{2}{\sqrt 5-\sqrt3}=\frac{2(\sqrt 5+\sqrt3)}{(\sqrt 5-\sqrt3)(\sqrt 5+\sqrt3)}=\frac{2(\sqrt 5+\sqrt3)}{5-3}=\sqrt 5+\sqrt3 \end{aligned}$