(sqrt (49 + 20sqrt6)) ^ (sqrt (asqrt (asqrt (a ... oo) + (5-2sqrt6) ^ (x ^ 2 + x-3 - sqrt (xsqrt (xsqrt (x ... oo) ))) = 10 on a = x ^ 2-3, llavors x és?

Resposta:

#x = 2 #

Trucades #sqrt 49 + 20 sqrt 6 = 5 + 2 sqrt 6 = beta # tenim

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

per

#sqrt (asqrt (asqrt (a … oo))) = 1 i

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

i tal

# a = x ^ 2-3 #

però

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

i llavors

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

llavors

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

o bé

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

llavors #x = 2 #