SOLUTION: 16+sqrt(16+sqrt(16+sqrt(16+sqrt(16+(sqrt(16....)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 16+sqrt(16+sqrt(16+sqrt(16+sqrt(16+(sqrt(16....)      Log On


   

Question 983935: 16+sqrt(16+sqrt(16+sqrt(16+sqrt(16+(sqrt(16....)
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
x = 16+sqrt(x)
x- sqrt(x) -16 = 0
y = sqrt(x)
y^2 - y -16 = 0
We'll only accept the positive solution since it would make sense that adding 16 to a square root will result positively.

y+=+%281+%2B+sqrt%281+-+4%28-16%29%29%29+%2F+2
+y+=+%281%2Bsqrt%2865%29%29%2F2
sqrt%28x%29+=+%281%2Bsqrt%2865%29%29%2F2
+x+=+%28%281%2Bsqrt%2865%29%29%2F2%29%5E2+=+20.53 <--- answer