Kakšne so rešitve za kvadratno enačbo (5y + 6) ^ 2 = 24?

Odgovor:

# y_1 = (- 2sqrt6-6) / 5 #

# y_2 = (2sqrt6-6) / 5 #

Pojasnilo:

# (5y + 6) ^ 2 = 24 #

# 25y ^ 2 + 60y + 36 = 24 #

# 25y ^ 2 + 60y + 36-24 = 0 #

# 25y ^ 2 + 60y + 12 = 0 #

# "spomnimo:" #

#a y ^ 2 + z + c = 0 #

# Delta = b ^ 2-4ac #

# a = 25, b = 60, c = 12 #

# Delta = 60 ^ 2-4 * 25 * 12 #

# Delta = 3600-1200 = 2400 #

#Delta = + - 20sqrt6 #

# y_1 = (- b-Delta) / (2a) = (- 60-20sqrt 6) / (2 * 25) = (- 6iskanje (0) -2kn (0) sqrt 6) / (5kkaz (0)) #

# y_1 = (- 2sqrt6-6) / 5 #

# y_2 = (- b-Delta) / (2a) = (- 60 + 20sqrt 6) / (2 * 25) = (- 6zaključi (0) + 2prekliči (0) sqrt 6) / (5kkaz (0)) #

# y_2 = (2sqrt6-6) / 5 #