(Sqrt (5+) sqrt (3)) / (sqrt (3+) sqrt (3+) sqrt (5)) - (sqrt (5) sqrt (3)) / (sqrt (3+) sqrt nedir (3) sqrt (5))?

Cevap:

#2/7#

Açıklama:

Alıyoruz

# 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) #

# = ((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) #

# = (iptal et (2sqrt15) -5 + 2 * 3cancel (-sqrt15) - iptal (2sqrt15) -5 + 2 * 3 + iptal (sqrt15)) / (12-5) #

#=(-10+12)/7#

#=2/7#

Payda ise,

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

o zaman cevap değişecek.