(sqrt (49 + 20sqrt6)) ^ (sqrt (asqrt (asqrt (a ... oo) + (5-2sqrt6) ^ (x ^ 2 + x-3 - sqrt (xsqrt (xsqrt (x ... oo) ))) = 10 kde a = x ^ 2-3, potom x je?

odpoveď:

#x = 2 #

povolania #sqrt 49 + 20 sqrt 6 = 5 + 2 sqrt 6 = beta # máme

# (5 + 2 sqrt 6) ^ 1+ (5- 2 sqrt 6) ^ 1 = 10 #

pre

#sqrt (asqrt (asqrt (a … oo))) = 1 # a

# x ^ 2 + x-3 - sqrt (xsqrt (xsqrt (x … oo)) = 1 #

a také

# A = x ^ 2-3 #

ale

#sqrt (asqrt (asqrt (a … oo))) = a ^ (1/2 + 1/4 + 1/8 + cdots + 1/2 ^ k + cdots) = a ^ 1 = 1 #

a potom

# 1 = x ^ 2-3 rArr x = 2 #

potom

# x ^ 2 + x-3 - sqrt (xsqrt (xsqrt (x … oo)) = 1 #

alebo

# 1 + 2- sqrt (2sqrt (2sqrt (2 … oo)) = 1 #

potom #x = 2 #