Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Wat is de oplossing van de irrationale vergelijking $https://latex.codecogs.com/png.image?\inline \dpi{120}\sqrt{x+\sqrt{2x+6}}-\sqrt{x-\sqrt{2x+6}}=2$	A. 1
B. 2
C. 3
D. 4
E. 5

What is the solution of the equation $\sqrt{x+\sqrt{2x+6}}-\sqrt{x-\sqrt{2x+6}}=2$	A. 1
	B. 2
	C. 3
	D. 4
	E. 5

$\\\sqrt{x+\sqrt{2x+6}}-\sqrt{x-\sqrt{2x+6}}=2\\\Rightarrow\;x+\sqrt{2x+6}-2\sqrt{x+\sqrt{2x+6}}.\sqrt{x-\sqrt{2x+6}}+x-\sqrt{2x+6}=4\\\Leftrightarrow\;2x-4=2\sqrt{x+\sqrt{2x+6}}.\sqrt{x-\sqrt{2x+6}}\\\Leftrightarrow\;x-2=\sqrt{x+\sqrt{2x+6}}.\sqrt{x-\sqrt{2x+6}}\\\Rightarrow\;x^2-4x+4=(x+\sqrt{2x+6}).(x-\sqrt{2x+6})\\\Leftrightarrow\;x^2-4x+4=x^2-2x-6\\\Leftrightarrow\;-2x=-10\\\Leftrightarrow\;x=5$