Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\inline \dpi{120}\\\frac 1x \: + \: x \, = 3\\\\\frac{1}{x^2}+x^2 = \: ?$	A. 3
	B. 5
	C. 7
	D. 9
	E. een irrationaal getal

[ 3-7520 - op net sinds 20.9.13_(E)-21.11.2024 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\inline \dpi{120}\\\frac 1x \: + \: x \, = 3\\\\\frac{1}{x^2}+x^2 = \: ?$	A. 3
	B. 5
	C. 7
	D. 9
	E. an irrational number

Oplossing - Solution

$\\\frac{1}{x}+x=3\;\Rightarrow\;(\frac{1}{x}+x)^2=9\;\Rightarrow\;\frac{1}{x^2}+2\cdot\frac{1}{x}\cdot x+x^2=9\;\Rightarrow\;\frac{1}{x^2}+x^2=9-2=\cdots$