Aké sú možné hodnoty x a y, ak y ^ 2 = x ^ 2-64 a 3y = x + 8 ??

odpoveď:

# (x, y) = (-8, 0), (10, 6)

vysvetlenie:

# 3y = x + 8 => x = 3y - 8 #

# y ^ 2 = x ^ 2 - 64 #

# y ^ 2 = (3y - 8) ^ 2 - 64 #

# y ^ 2 = 9y ^ 2 - 48 hodín + 64 - 64 #

# 8y ^ 2 - 48y = 0 #

# 8y (y - 6) = 0 #

#y = 0, 6 #

# x = 3y - 8 a y = 0 #:

# x = 0 - 8 #

# = -8#

# x = 3y - 8 a y = 6 #:

# x = 3 xx 6 - 8 #

# x = 10 #

# (x, y) = (-8, 0), (10, 6) #

odpoveď:

#(-8,0),(10,6)#

vysvetlenie:

# Y ^ 2 = x ^ 2-48to (1) #

# 3y = x + 8to (2) #

# "z rovnice" (2) "môžeme vyjadriť x z hľadiska y" #

# RArrx = 3r-8to (3) #

# "nahradiť" x = 3y-8 "v rovnici" (1) #

# rArry ^ 2 = (3y-8) ^ 2-64larrcolor (modrý) "expand" (3y-8) ^ 2 #

# Rarr ^ 2 = 9Y ^ 2-48ycancel (64) zrušiť (-64) #

# RArr8y ^ 2-48 = 0larrcolor (modrá) "factorise" #

# 8Y (y-6) = 0 #

# "priradiť každý faktor k nule a vyriešiť pre y" #

# 8Y = 0rArry = 0 #

# Y-6 = 0rArry = 6 #

# "nahradiť tieto hodnoty do rovnice" (3) #

# Y = 0rArrx = -8rArr (-8,0) #

# Y = 6rArrx = 18-8 = 10rArr (10,6) #

Graf {(y ^ 2-x ^ 2 + 64) (Y-1 / 3x-8/3) ((x + 8) ^ 2 + (y-0) ^ 2-0,04) ((x-10), ^ 2+ (y-6) ^ 2-0.04) = 0 -20, 20, -10, 10}