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What is the value of x for which \(\sqrt{x + \sqrt{x + \sqrt{x + \ldots}}} = 5\)

 Jul 8, 2020
 #1
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[ sqrt( x + sqrt( x + sqrt( x = ... ]  =  5

 

Square both sides:

x + [ sqrt( x + sqrt( x + sqrt( x = ... ]   =  25

 

Since  [ sqrt( x + sqrt( x + sqrt( x = ... ]  =  5:

 

x + 5  =  25

      x  =  20

 Jul 8, 2020
 #2
avatar+793 
0

Thank you!

AnimalMaster  Jul 8, 2020

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