SOLUTION: If sqrt5 = 2 + 1/a, show that a = 4 + 1/a. Thank you.

Question 1118064: If sqrt5 = 2 + 1/a, show that a = 4 + 1/a. Thank you.
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
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Let's rationalize a:
(1)

Now

But we can use (1) to write :
<� the final expression is

Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
This problem was solved yesterday at this link

https://www.algebra.com/algebra/homework/equations/Equations.faq.question.1118033.html

https://www.algebra.com/algebra/homework/equations/Equations.faq.question.1118033.html

Three solutions were presented at that link:

        one by @josgarithmetic - incorrect (he erased it later);

        Other by me - very similar to that displayed in the post by @Math_helper, and explained in all details;

        and the third by @MathTherapy - even better than my, because it was shorter.

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