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. $\frac12$
	B. 2
	C. $\frac23$
	D. $\frac25$
	E. $\frac65$

[ 5-6340 - op net sinds 25.2.16-(E)-15.11.2024 ]

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. $\frac12$
	B. 2
	C. $\frac23$
	D. $\frac25$
	E. $\frac65$

Oplossing - Solution

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

$https://latex.codecogs.com/png.image?\dpi{110}\frac{4^{-\sqrt 3}+5\cdot0,5^{\sqrt{12}}}{\left (2^{\, 2-\sqrt 3} - 2^{-\sqrt 3} \right )^2}$ is gelijk aan	A. \(\frac12\)
	B. 2
	C. \(\frac23\)
	D. \(\frac25\)
	E. \(\frac65\)

$\frac{4^{-\sqrt 3}+5\cdot0.5^{\sqrt{12}}}{\left (2^{\, 2-\sqrt 3} - 2^{-\sqrt 3} \right )^2}$ is equal to	A. \(\frac12\)
	B. 2
	C. \(\frac23\)
	D. \(\frac25\)
	E. \(\frac65\)