Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

${\color{DarkBlue} x+\frac1x=3\quad\Rightarrow \quad x^2+\frac{1}{x^2}=?}$	A. 1
	B. 2
	C. 3
	D. 7
	E. 9

[ 3-0408 - op net sinds 8.3.13-(E)-21.11.2024 ]

Translation in E N G L I S H

${\color{DarkBlue} x+\frac1x=3\quad\Rightarrow \quad x^2+\frac{1}{x^2}=?}$	A. 1
	B. 2
	C. 3
	D. 7
	E. 9

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\\x+\frac1x=3\; \Rightarrow \; \left ( x+\frac1x \right )^2=3^2\; \Rightarrow\; x^2+2.x.\frac1x+\frac{1}{x^2}=9\\{\color{Green} .\qquad\qquad\qquad}x^2+2+\frac{1}{x^2}=9\; \Rightarrow \; x^2+\frac{1}{x^2}=\cdots$