Question

pls answer fast ..
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Answer 1

a=(3+√5)/2
1/a = 1/[(3+√5)/2]

=> 1/a = 2/(3+√5)

=> 1/a = 2(3-√5)/(3+√5)(3-√5)
rationalizing the denominator

=> 1/a = (6-2√5)/3²-(√5)²
=> 1/a = (6-2√5)/9-5
=> 1/a = (6-2√5)/4


(a+1/a)² = a²+1/a ²+2


=> [(3+√5)/2 + (6-2√5)/4] = a²+1/a²+2

=> [2(3+√5)/(2)2 + (6-2√5)/4] = a²+1/a²+2
Making denominator equal


=> (6+2√5+6-2√5)/4 = a²+1/a²+2
=> 12/4 = a²+1/a²+2

=> 3 = a²+1/a²+2

=> 3-2 = a²+1/a²

=> 1 = a²+1/a²