Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\large \dpi{110}\frac {\sqrt 5+\sqrt 3} {\sqrt 5-\sqrt 3}$ is gelijk aan	A. 1
	B. − 1
	C. 4 +
	D. 4 + 2
	E. geen van de vorige

[ 4-1794 - op net sinds 10.2.13-(E)-3.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\large \dpi{110}\frac {\sqrt 5+\sqrt 3} {\sqrt 5-\sqrt 3}$ is equal to	A. 1
	B. − 1
	C. 4 +
	D. 4 + 2
	E. none of the above

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\frac {\sqrt 5+\sqrt 3} {\sqrt 5-\sqrt 3}=\frac{(\sqrt 5+\sqrt 3)(\sqrt 5+\sqrt 3)}{(\sqrt 5-\sqrt 3)(\sqrt 5+\sqrt 3)}\\=\frac{(\sqrt 5+\sqrt 3)^2}{5-3}=\frac{5+2\sqrt5\, \sqrt3+3}{2}=\frac{8+2\sqrt{15}}{2}=4+\sqrt{15}$