Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Eén van de oplossingen van de rationale vergelijking $https://latex.codecogs.com/png.image?\dpi{110}\frac{x^2}{(x-2)^2}+\frac{x^2}{(x+2)^2}=2$ is	A. $\large\boldsymbol{\frac {\sqrt 3} {2} }$
	B. $\large\boldsymbol{\frac {\sqrt 3} {3} }$
	C. $\large\boldsymbol{\frac {3\sqrt 3} {2} }$
	D. $\large\boldsymbol{\frac {2\sqrt 3} {3} }$
	E. $\large\boldsymbol{\frac {2\sqrt 2} {3} }$

[ 5-8440 - op net sinds 2.3.2019-(E)-19.12.2023 ]

Translation in E N G L I S H

One of the solutions of the equation $https://latex.codecogs.com/png.image?\dpi{110}\frac{x^2}{(x-2)^2}+\frac{x^2}{(x+2)^2}=2$ is	A. $\boldsymbol{\frac {\sqrt3}{2}}$
	B. $\boldsymbol{\frac {\sqrt3}{3}}$
	C. $\boldsymbol{\frac {3\sqrt3}{2}}$
	D. $\boldsymbol{\frac {2\sqrt3}{3}}$
	E. $\boldsymbol{\frac {2\sqrt2}{3}}$

Oplossing - Solution

$\frac{x^2}{(x-2)^2}+\frac{x^2}{(x+2)^2}=2\\\frac{x^2[(x+2)^2+(x-2)^2]}{(x-2)^2.(x+2)^2}=2\\\frac{x^2[x^2+4x+4+x^2-4x+4]}{[(x-2)(x+2)\]^2}=2\\\frac{x^2[2x^2+8]}{(x^2-4)^2}=2\\\frac{x^4+4x^2}{(x^2-4)^2}=1$
$\\t=x^2\;\;\wedge\;\;t^2+4t=(t-4)^2\\t=x^2\;\;\wedge\;\;t^2+4t=t^2-8t+16\\t=x^2\;\;\wedge\;\;12t=16\\t=x^2\;\;\wedge\;\;t=\frac{16}{12}=\frac43=\frac49.3\\x=\pm\sqrt{\frac49.3}=\pm\frac23\sqrt3$

Eén van de oplossingen van de rationale vergelijking $https://latex.codecogs.com/png.image?\dpi{110}\frac{x^2}{(x-2)^2}+\frac{x^2}{(x+2)^2}=2$ is	A. \(\large\boldsymbol{\frac {\sqrt 3} {2} }\)
	B. \(\large\boldsymbol{\frac {\sqrt 3} {3} }\)
	C. \(\large\boldsymbol{\frac {3\sqrt 3} {2} }\)
	D. \(\large\boldsymbol{\frac {2\sqrt 3} {3} }\)
	E. \(\large\boldsymbol{\frac {2\sqrt 2} {3} }\)

One of the solutions of the equation $https://latex.codecogs.com/png.image?\dpi{110}\frac{x^2}{(x-2)^2}+\frac{x^2}{(x+2)^2}=2$ is	A. \(\boldsymbol{\frac {\sqrt3}{2}}\)
	B. \(\boldsymbol{\frac {\sqrt3}{3}}\)
	C. \(\boldsymbol{\frac {3\sqrt3}{2}}\)
	D. \(\boldsymbol{\frac {2\sqrt3}{3}}\)
	E. \(\boldsymbol{\frac {2\sqrt2}{3}}\)