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avatar+143 

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? 

 Jul 13, 2021
 #1
avatar+121062 
+3

Note  that  the  given expression  = 9

 

Square  both sides

 

x  +  given expression  =      81

 

x  +  9    =   81

 

x   = 81  - 9    =    72

 

 

cool cool cool

 Jul 13, 2021
 #2
avatar+143 
+1

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

 

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

HighSchoolDx  Jul 13, 2021
 #3
avatar+121062 
+1

No prob....I just hope it's correct!!!!   (HAHAHA!!!)

 

 

cool cool cool

CPhill  Jul 13, 2021
 #4
avatar
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 :/

 Jul 13, 2021
edited by Guest  Jul 13, 2021
edited by Guest  Jul 13, 2021

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