Ratkaise ... 5 - x = sqrt (x + sqrt (x + sqrt (x + sqrtx))) Etsi x?

Ratkaise ... 5 - x = sqrt (x + sqrt (x + sqrt (x + sqrtx))) Etsi x?
Anonim

Vastaus:

Vastaus on # = 5-sqrt5 #

Selitys:

Päästää # Y = sqrt (x + sqrt (x + sqrt (x + sqrt (x + ….)))) #

neliöimistä, # Y ^ 2 = x + sqrt (x + sqrt (x + sqrt (x + sqrt (x + ….)))) #

# Y ^ 2 = x + y #

Kuten, # Y = 5 x #

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

#y = + - sqrt5 #

Siksi, # Y ^ 2 = x + y #

# 5 = x + sqrt5 #

# X = 5-sqrt5 #