Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$6+\sqrt2\,x=7-x$ heeft als oplossing	A. $\boldsymbol{\sqrt 2 - 1 }$
	B. $\boldsymbol{1 - \sqrt 2 }$
	C. $\large\boldsymbol{\frac {\sqrt 3} {3} }$
	D. $\large\boldsymbol{\frac {\sqrt 2} {4} }$
	E. $\large\boldsymbol{\frac 12 }$
	F. $\large\boldsymbol{\pm \frac {\sqrt{13}} {3} }$

[ 4-4163 - op net sinds 28.12.15-(E)-6.11.2024 ]

What is the solution of $6+\sqrt2\,x=7-x$ See above

6 +

x = 7 − x

⇔ v2puur

x + x = 7 − 6
⇔ ( v2puur

+ 1)x = 1
⇔ $x=\frac {1} {\sqrt2\,+\,1}=\frac{\sqrt2-1}{(\sqrt2+1)(\sqrt2-1)}=\frac{\sqrt2-1}{2-1}=\sqrt2 - 1 $

$6+\sqrt2\,x=7-x$ heeft als oplossing	A. \(\boldsymbol{\sqrt 2 - 1 }\)
	B. \(\boldsymbol{1 - \sqrt 2 }\)
	C. \(\large\boldsymbol{\frac {\sqrt 3} {3} }\)
	D. \(\large\boldsymbol{\frac {\sqrt 2} {4} }\)
	E. \(\large\boldsymbol{\frac 12 }\)
	F. \(\large\boldsymbol{\pm \frac {\sqrt{13}} {3} }\)