When graphed, the function is valid only from x=5 to 20 as beyond this domain imaginary numbers enter. The value monotonically increases from 2.55340368400053 to 2.581183401292867 and is crossed by the line y=x only once.
DEFDBL AZ
CLS
FOR x = 2.5623043215017# TO 2.5623043215018# STEP .00000000000001#
PRINT x, SQR(5 + SQR(5  SQR(5 + SQR(5  SQR(5 + x)))))  x
NEXT x
finds that the answer is approximately 2.56230432150173.
the program was changed each time the next decimal place was sought, narrowing the possibilities.

Posted by Charlie
on 20121217 17:44:44 