Question

If a = 3+ root 5÷2, then find the value of a+1/a.

Answer 1

Answer:

Step-by-step explanation= (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

hope this helps