Question

if a =3+√5/2 find a^2 + 1/a^2

Answer 1

a= (3+√5)/21/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+2Making 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



hope this helps