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

Válasz:

#x = 2 #

Hívás #sqrt 49 + 20 sqrt 6 = 5 + 2 sqrt 6 = béta # nekünk van

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

mert

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

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

és így

# A = x ^ 2-3 #

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

és akkor

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

azután

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

vagy

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

azután #x = 2 #