Question

If a=(3+✓5)/2, find the value of (a+1/a)​

Answer 1

Answer:

given: a = 3 + √5 / 2

Therefore,

1 / a = 2 / 3 + √5

= 2 × ( 3 - √5 ) / ( 3 + √5 ) × ( 3 - √5 )

= 2 × ( 3 - √5 ) / ( 3 )² - ( √5 )²

= 3 - √5 / 2a + 1 /a

= 3 + √5 /2 + 3 - √5 /2

= 6 / 2

a + 1/a = 3

Using identity: (a + b)² = a² + 2ab + b²

(a + 1 /a)² = a² + 1/a² + 2 (a) × (1/a)

=> (a + 1 /a)² - 2 (a) × (1/a) = a² + 1/a²

=> (3)² - 2 = a² + 1/a

=> (3)² - 2 = a² + 1/a²

=> (9) - 2 = a² + 1/a²

7 = a² + 1 /a²

Thus, answer to your question is 7.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

hope it helps you best of luck