Question

Find the value of? answer me please ​

Answer 1

Step-by-step explanation:

a= (3 +√5)/2

a² = [(3 +√5)/2]²

= (9 + 6√5 + 5)/4

= (14 + 6√5)/4

[(a + b)² = a² + 2ab + b²]

1/a² = 1/(14 + 6√5)/4

= 4/(14 + 6√5)

(Rationalising 4/(14 + 6√5))

= 4/(14 + 6√5) × (14 - 6√5)/(14 - 6√5)

= [4(14 - 6√5)]/[(14)² - (6√5)²

= (56 - 24√5)/(196 - 180)

= (56 - 24√5)/(16)

a² + 1/a² = (14 + 6√5)/4 + (56 - 24√5)/16

= 4(14 + 6√5)/16 + (56 - 24√5)/16

= (56 + 24√5)/16 + (56 - 24√5)/16

= (56 + 24√5 + 56 - 24√5)/16

= (112)/16

= 7 [Answer]