I have attached the question I need help, question 5, and really not sure how to go about,
any help / tips appreciated
Begin with writing out a little bit of the continued fraction:
Now, you are asked to show that . This is obvious. Just replace everything under the top 1 of the continued fraction by y (since it is equal to y).
So, how can you solve the rest of it? Well, solve for . If you multiply everything by , you get . Treat as a constant and you have a quadratic of one variable. Solve for . Then . Just plug in whatever you get as your answer.