92.6k views
2 votes
For an irrational number x = 3 + 2√2 , find out what will be the nature of the number x + 1/x

User Desolate
by
7.9k points

1 Answer

5 votes
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))
User Vipergtsrz
by
8.9k points