Solve... #5 - x = sqrt(x + sqrt(x + sqrt(x + sqrtx)))# Find #x#?

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Answer 1 · 2017-11-22T09:22:21

The answer is #=5-sqrt5#

Let #y=sqrt(x+sqrt(x+sqrt(x+sqrt(x+....))))#

Squaring,

#y^2=x+sqrt(x+sqrt(x+sqrt(x+sqrt(x+....))))#

#y^2=x+y#

As,

#y=5-x#

#y^2=x+5-x=5#

#y=+-sqrt5#

Therefore,

#y^2=x+y#

#5=x+sqrt5#

#x=5-sqrt5#