SOLUTION: If the expression x=sqrt(2+sqrt(2+sqrt(2+sqrt(2+...) extends to an infinite number of roots and converges to a positive number x, what is x?

Question 1134096: If the expression x=sqrt(2+sqrt(2+sqrt(2+sqrt(2+...) extends to an infinite number of roots and converges to a positive number x, what is x?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!



Square both sides:



Subtract 2 from both sides:



The right side is the same as the right side of the
original equation so it's just x:







x+1=0;  x-2=0
  x=-1;   x=2

We discard the negative answer because the radical
always means the POSITIVE square root.

Answer: x=2

Edwin

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