Løs ... 5 - x = sqrt (x + sqrt (x + sqrt (x + sqrtx))) Find x?

Løs ... 5 - x = sqrt (x + sqrt (x + sqrt (x + sqrtx))) Find x?
Anonim

Svar:

Svaret er # = 5-sqrt5 #

Forklaring:

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

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

# Y ^ 2 = x + y #

Som, # Y = 5-x #

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

#Y = + - sqrt5 #

Derfor, # Y ^ 2 = x + y #

# 5 = x + sqrt5 #

# X = 5-sqrt5 #