Was ist (sq (5+)) sqrt (3)) / (sqrt (3+) sqrt (3+) sqrt (5)) - (sqrt (5) sqrt (3)) / (sqrt (3+) sqrt) (3-) Quadrat (5))?

Antworten:

#2/7#

Wir nehmen, # A = (sqrt5 + sqrt3) / (sqrt3 + sqrt3 + sqrt5) - (sqrt5-sqrt3) / (sqrt3 + sqrt3-sqrt5) #

# = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - (sqrt5-sqrt3) / (2sqrt3-sqrt5) #

# = ((sqrt5 + sqrt3) (2sqrt3-sqrt5) - (sqrt5-sqrt3) (2sqrt3 + sqrt5)) / ((2sqrt3 + sqrt5) (2sqrt3-sqrt5) #

# = ((2sqrt15-5 + 2 * 3-sqrt15) - (2sqrt15 + 5-2 * 3-sqrt15)) / ((2sqrt3) ^ 2- (sqrt5) ^ 2) #

# = (Abbruch (2sqrt15) -5 + 2 * 3cancel (-sqrt15) - Abbruch (2sqrt15) -5 + 2 * 3 + Abbrechen (sqrt15)) / (12-5) #

#=(-10+12)/7#

#=2/7#

Beachten Sie das, wenn in den Nennern sind

# (sqrt3 + sqrt (3 + sqrt5)) und (sqrt3 + sqrt (3-sqrt5)) #

dann wird die Antwort sich ändern.