find x when

$\sqrt{x+\!\sqrt{x+\!\sqrt{x+\!\sqrt{x+\cdots}}}}=9$

I think i should multiply by x, but then that would just give $x\sqrt{x+\!\sqrt{x+\!\sqrt{x+\!\sqrt{x+\cdots}}}}=9x.$ thoughts?

HighSchoolDx Jul 13, 2021

#1**+3 **

Note that the given expression = 9

Square both sides

x + given expression = 81

x + 9 = 81

x = 81 - 9 = 72

CPhill Jul 13, 2021

#2**+1 **

THANK YOU SO MUCH!!!!!!!!!

I had no idea it was that simple... ELEGANT solution

HighSchoolDx
Jul 13, 2021

#4**0 **

im thinking of another way...what if we say that the sqrt thingy is a variable...the things behind it are the same

P. S. an aops algebra 1(or another book) has a similar problem

also im bored theres no questions being post :/

Guest Jul 13, 2021

edited by
Guest
Jul 13, 2021

edited by Guest Jul 13, 2021

edited by Guest Jul 13, 2021