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

Algebra ->  Equations -> SOLUTION: If sqrt5 = 2 + 1/a, show that a = 4 + 1/a. Thank you.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%285%29+=+2+%2B+1%2Fa+ —> +a+=+1%2F%28%28sqrt%285%29%29-2%29++
Let's rationalize a:
(1)

Now
+4+%2B+1%2Fa+=++4+%2B+1%2F%28%28sqrt%285%29%29+%2B+2%29+
But we can use (1) to write :
<— the final expression is +highlight%28a%29+

Answer by ikleyn(52893) About Me  (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.