Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{4^{-\sqrt 3}+5\cdot0,5^{\sqrt{12}}}{\left (2^{\, 2-\sqrt 3} - 2^{-\sqrt 3} \right )^2}$ is gelijk aan	A.
	B. 2
	C.
	D.
	E.

[ 5-6340 - op net sinds 25.2.16-(E)-4.11.2023 ]

Translation in E N G L I S H

$\frac{4^{-\sqrt 3}+5\cdot0.5^{\sqrt{12}}}{\left (2^{\, 2-\sqrt 3} - 2^{-\sqrt 3} \right )^2}$ is equal to	A.
	B. 2
	C.
	D.
	E.

Oplossing - Solution

$\\\frac{4^{-\sqrt 3}+5\cdot0,5^{\sqrt{12}}}{\left(2^{\,2-\sqrt 3}-2^{-\sqrt 3}\right)^2}=\frac{(2^2)^{-\sqrt 3}+5\cdot(2^{-1})^{\sqrt{4.3}}}{\left(2^2.2^{\,-\sqrt 3}-2^{-\sqrt 3}\right)^2}\\=\frac{2^{-2\sqrt3}+5.2^{-2\sqrt3}}{\left[2^{-\sqrt3}(2^2-1)\right]^2}=\frac{6.2^{-2\sqrt3}}{2^{-2\sqrt3}.3^2}=\frac69=\frac23$