Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Wat is de oplossing van de vergelijking $(x-\sqrt 2)^2 + (x + \sqrt 3)^2 = 2x^2+3$	A. $\small\boldsymbol{\sqrt 2 + \sqrt 3}$
	B. $\small\boldsymbol{\sqrt 2 - \sqrt 3}$
	C. $\small\boldsymbol{\sqrt 3 - \sqrt 2}$
	D. $\small\boldsymbol{-\,\sqrt 2 - \sqrt 3}$
	E. $\boldsymbol{\frac {\sqrt 2\:-\:\sqrt 3} {5} }$
	F. $\boldsymbol{\frac {\sqrt 2\:+\:\sqrt 3} {5} }$

[ 3-4892 - op net sinds 3.6.2020-()-25.6.2024 ]

Translation in E N G L I S H

IN CONSTRUCTION

Oplossing - Solution

$(x-\sqrt 2)^2+(x+\sqrt 3)^2=2x^2+3\\\Leftrightarrow x^2-2x\sqrt2+2+x^2+2x\sqrt3+3=2x^2+3\\\Leftrightarrow 2x(\sqrt3-\sqrt2)=-2\\\Leftrightarrow x=\frac{-1}{\sqrt3-\sqrt2}\\\Leftrightarrow x=\frac{-(\sqrt3+\sqrt2)}{(\sqrt3-\sqrt2)(\sqrt3+\sqrt2)}\\\Leftrightarrow x=\frac{-\sqrt2-\sqrt2}{3-2}\\\Leftrightarrow x=-\sqrt2-\sqrt3$

Wat is de oplossing van de vergelijking $(x-\sqrt 2)^2 + (x + \sqrt 3)^2 = 2x^2+3$	A. \(\small\boldsymbol{\sqrt 2 + \sqrt 3}\)
	B. \(\small\boldsymbol{\sqrt 2 - \sqrt 3}\)
	C. \(\small\boldsymbol{\sqrt 3 - \sqrt 2}\)
	D. \(\small\boldsymbol{-\,\sqrt 2 - \sqrt 3}\)
	E. \(\boldsymbol{\frac {\sqrt 2\:-\:\sqrt 3} {5} }\)
	F. \(\boldsymbol{\frac {\sqrt 2\:+\:\sqrt 3} {5} }\)