Question

if a=3+√5/2,then find the value of a²+1/a²​

Answer 1

Answer: 7

Step by step explanation:

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 / 2

a + 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)

Subtract 2 from both sides,

=> (3)² - 2 = ( a + 1 /a )² + 2 (a) × (1/a) - 2  

9 - 2 = (a + 1 /a)²

7 = (a + 1 /a)²

Thus, answer to your question is 7.

Answer 2

Answer:

a2+1/a2

(3+√5/2)2 +1/(3+√5/2)2

9+5/4+3√5+1/9+5/4+3√4

(36+5/4)