Aké sú riešenia kvadratickej rovnice (5y + 6) ^ 2 = 24?

Aké sú riešenia kvadratickej rovnice (5y + 6) ^ 2 = 24?
Anonim

odpoveď:

# Y_1 = (- 2sqrt6-6) / 5 #

# Y_2 = (2sqrt6-6) / 5 #

vysvetlenie:

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

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

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

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

# "Pripomeňme si:" #

#a y ^ 2 + o + 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) = (- 6 (2) 2 (1) sqrt 6) / (5cancel (0)) #

# Y_1 = (- 2sqrt6-6) / 5 #

# y_2 = (- b-Delta) / (2a) = (- 60 + 20sqrt 6) / (2 * 25) = (- 6 centov (0) + 2 číslo (0) sqrt 6) / (5cancel (0)) #

# Y_2 = (2sqrt6-6) / 5 #