Question

For an irrational number x = 3 + 2√2 , find out what will be the nature of the number x + 1/x

Answer 1

For this case we have the following number:

`x = 3 + 2 √(2)`
We have the following expression:

`x + (1)/(x)`
Substituting values and rewriting we have:

`1 + (1)/(3 + 2 √(2)) ((3 + 2 √(2))^2 + 1)/(3 + 2 √(2)) (3^2 + 24√(2) + 8)/(3 + 2 √(2)) (9 + 24√(2) + 8 )/(3 + 2 √(2)) (17 + 24√(2))/(3 + 2 √(2))`
Answer:
The nature of the number x + 1 / x will be:

`(17 + 24√(2))/(3 + 2 √(2))`