Question

if a = 9-4√5, find the value of a ^2+1/a^2

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Hence, the value of a^2 + 1/a^2 is 332.

Step-by-step explanation:

Given: a = 9 + 4√5

Then:

(1/a) = (1/9 + 4√5) * (9 - 4√5)/(9 - 4√5)

       = [(9 - 4√5)]/(9)² - (4√5)²

       = 9 - 4√5/81 - 80

       = 9 - 4√5

Then:

a + 1/a = 9 + 4√5 + 9 - 4√5

           = 18

So, a + 1/a = 18

On Squaring both sides, we get

⇒ (a + 1/a)² = 18²

⇒ a² + 1/a² + 2 = 324

⇒ a² + 1/a² = 322

Hence, the value of a^2 + 1/a^2 is 332.

Hope it helps!