If x = ?3 + 1 and y = ?3 - 1 , then the value of (x2 + y2) is: ?3 - 1 ?3 + 1 10

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Question
If x = √3 + 1 and y = √3 - 1 , then the value of (x² + y²) is:

√3 - 1 √3 + 1
Options
A. 10
B. 13
C. 14
D. 15

Correct Answer

14

Explanation

x =	(√3 + 1)	x	(√3 + 1)	=	(√3 + 1)²	=	3 + 1 + 2√3	= 2 + √3.
	(√3 - 1)		(√3 + 1)		(3 - 1)		2

y =	(√3 - 1)	x	(√3 - 1)	=	(√3 - 1)²	=	3 + 1 - 2√3	= 2 - √3.
	(√3 + 1)		(√3 - 1)		(3 - 1)		2

∴ x² + y² = (2 + √3)² + (2 - √3)²

= 2(4 + 3)

= 14

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