Determine the exact value of √(10 + √(10 + √(10 + ....))) it goes on forever

Show all steps and explain most of them

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- Nov 7th 2009, 05:41 AMshane99Nested roots
Determine the exact value of √(10 + √(10 + √(10 + ....))) it goes on forever

Show all steps and explain most of them - Nov 7th 2009, 07:03 AMramiee2010
let $\displaystyle x= \sqrt{10+\sqrt{10+\sqrt{10+......}}} $

therefore

$\displaystyle x= \sqrt{10+x} $

taking square both side

$\displaystyle x^2= (10+x) $

$\displaystyle x^2-x-10=0$

now solve the quadratic equation ......... - Nov 7th 2009, 12:08 PMmr fantastic
No, that's not how it works. You do not make demands like that.

show what*You*can do and then say where*you*stuck.*you're*

I see you've been given a massive start on how to do this question. So now it's your turn. If you need more help, say what you've done and where you get stuck.