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Let $x$ = (√5 + 1)/(√5 − 1) and $y$ = (√5 − 1)/(√5 + 1). Find $(x^{2} + y^{2}) / (x^{2} - y^{2})$ .

Competition practiceAlgebra

A7√5/15
B7/3
C3√5/7
D√5/3

Step-by-Step Solution

x

= (3 + √5)/2 and

y

= (3 − √5)/2, so

x + y = 3, x y = 1

and

x - y

= √5.

x^{2} + y^{2} = 9 - 2 = 7

and

x^{2} - y^{2} = 3

√5. The ratio is 7/(3√5) = 7√5/15.

Answer: A) 7√5/15

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