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If $x$ = (√5 + 1)/(√5 − 1) and $y$ = (√5 − 1)/(√5 + 1), find the value of $x + y$ .

Competition practiceNumber & Arithmetic

A3
B6
C5
D4

Step-by-Step Solution

Rationalising,

x

= (6 + 2√5)/4 = (3 + √5)/2 and

y

= (3 − √5)/2. Adding gives (3 + √5 + 3 − √5)/2 = 6/2 = 3.

Answer: A) 3

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