Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Het omgekeerde van $\sqrt5 - 2$ is	A. $2-\sqrt5$
	B. $2+\sqrt5$
	C. $-2-\sqrt5$
	D. $\boldsymbol{\frac {1} {\sqrt 5} - \frac 12 }$
	E. $\sqrt5-2$

[ 4-0801 - op net sinds 27.2.13-(E)-9.7.2024 ]

Translation in E N G L I S H

The inverse of $\sqrt5-2$ is	A. $2-\sqrt5$
	B. $2+\sqrt5$
	C. $-2-\sqrt5$
	D. $\boldsymbol{\frac {1} {\sqrt 5} - \frac 12 }$
	E. $\sqrt5-2$

Oplossing - Solution

1^ste manier :
$\frac{1}{\sqrt5-2}=\frac{1.(\sqrt5+2)}{(\sqrt5-2).(\sqrt5+2)}=\frac{\sqrt5+2}{(\sqrt5)^2-2^2}=\frac{\sqrt5+2}{5-4}=\sqrt5+2$
2^de manier :
$\text{Het antwoord is}\;2+\sqrt5\;\text{omdat het product 1 is.}$
Immers : $\\(\sqrt5-2)\cdot(2+\sqrt5)=(\sqrt5-2).(\sqrt5+2)=(\sqrt5)^2-2^2=5-4=1$

Het omgekeerde van \(\sqrt5 - 2\) is	A. \(2-\sqrt5\)
	B. \(2+\sqrt5\)
	C. \(-2-\sqrt5\)
	D. \(\boldsymbol{\frac {1} {\sqrt 5} - \frac 12 }\)
	E. \(\sqrt5-2\)

The inverse of \(\sqrt5-2\) is	A. \(2-\sqrt5\)
	B. \(2+\sqrt5\)
	C. \(-2-\sqrt5\)
	D. \(\boldsymbol{\frac {1} {\sqrt 5} - \frac 12 }\)
	E. \(\sqrt5-2\)