Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\sqrt{2}\; x+x=1$ is gelijkwaardig met	A. $\boldsymbol{x = \frac {1} {2\sqrt 2} }$
	B. $\boldsymbol{x = \frac {1} {\sqrt 2} }$
	C. $\boldsymbol{\sqrt 3\;x =1 }$
	D. $\boldsymbol{x = \frac {\sqrt 2} {4} }$
	E. $\boldsymbol{x = \sqrt 2 - 1 }$

[ 3,4-4165 - op net sinds 9.9.13-(E)-30.10.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\sqrt{2}\; x+x=1$ is equivalent with	A. $\boldsymbol{x = \frac {1} {2\sqrt 2} }$
	B. $\boldsymbol{x = \frac {1} {\sqrt 2} }$
	C. $\boldsymbol{\sqrt 3\;x =1 }$
	D. $\boldsymbol{x = \frac {\sqrt 2} {4} }$
	E. $\boldsymbol{x = \sqrt 2 - 1 }$

Oplossing - Solution

${\color{DarkGreen} \sqrt{2}\, x+x=1\; \Leftrightarrow \; \left ( \sqrt{2}+1 \right )x=1 \; \Leftrightarrow \; x=\frac{1}{\sqrt{2}+1}=\frac{\sqrt{2}-1}{(\sqrt{2}+1)(\sqrt{2}+1)}=\frac{\sqrt{2}-1}{2-1}=\cdots }$

$https://latex.codecogs.com/png.image?\dpi{110}\sqrt{2}\; x+x=1$ is gelijkwaardig met	A. \(\boldsymbol{x = \frac {1} {2\sqrt 2} }\)
	B. \(\boldsymbol{x = \frac {1} {\sqrt 2} }\)
	C. \(\boldsymbol{\sqrt 3\;x =1 }\)
	D. \(\boldsymbol{x = \frac {\sqrt 2} {4} }\)
	E. \(\boldsymbol{x = \sqrt 2 - 1 }\)

$https://latex.codecogs.com/png.image?\dpi{110}\sqrt{2}\; x+x=1$ is equivalent with	A. \(\boldsymbol{x = \frac {1} {2\sqrt 2} }\)
	B. \(\boldsymbol{x = \frac {1} {\sqrt 2} }\)
	C. \(\boldsymbol{\sqrt 3\;x =1 }\)
	D. \(\boldsymbol{x = \frac {\sqrt 2} {4} }\)
	E. \(\boldsymbol{x = \sqrt 2 - 1 }\)