Resoldre ... 5 - x = sqrt (x + sqrt (x + sqrt (x + sqrtx)) Trobeu x?

Resposta:

La resposta és # = 5-sqrt5 #

Explicació:

Deixar # y = sqrt (x + sqrt (x + sqrt (x + sqrt (x + ….))))

Quadrat, # y ^ 2 = x + sqrt (x + sqrt (x + sqrt (x + sqrt (x + ….)))) #

# y ^ 2 = x + y #

Com, # y = 5-x #

# y ^ 2 = x + 5-x = 5 #

#y = + - sqrt5 #

Per tant, # y ^ 2 = x + y #

# 5 = x + sqrt5 #

# x = 5-sqrt5 #