1

I can't find the answer to this problem

Find $y$ when

$y=\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5 + \ldots}}}}$

Any help is appreciated. Thank You

Community
  • 1
Rayyan Merchant
  • 109
  • 2
    You mean $y=\sqrt{5+\sqrt{5+\sqrt{5+\dots }}}$? If so, then Hint: Square the equation to get a quadratic expression in $y$. – lulu Nov 28 '15 at 00:15
  • Yes that is what I mean yes thank you – Rayyan Merchant Nov 28 '15 at 00:16
  • Sorry for that I didn't see that answer before I apologize for my mistake – Rayyan Merchant Nov 28 '15 at 00:23
  • IF the number exists then $y = \sqrt{5 + \sqrt{5+...}}$ Then $y^2 = 5 + \sqrt{5 + \sqrt{5+...}} $ then $y^2 = 5 + y$ so $y^2 - y - 5 = 0$. Use the quadraditic equation However, I'd be remiss if I didn't warn that just because one can write an expression doesn't mean it has a value. (Ex: x = 1+ 2 + 4 + 8 +... doesn't have an answer.) – fleablood Nov 28 '15 at 00:25
  • @RayyanMerchant No problem! The keyword was "nested radicals", and it takes practice to search the site; thanks for being a good sport :) – pjs36 Nov 28 '15 at 00:26
  • @fleablood Just to be goofy: https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF – Simply Beautiful Art Feb 01 '16 at 01:49

0 Answers0