Jaké jsou možné hodnoty x a y, pokud y ^ 2 = x ^ 2-64 a 3y = x + 8 ??

Odpovědět:

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

Vysvětlení:

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

# y ^ 2 = x ^ 2 - 64 #

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

# y ^ 2 = 9y ^ 2 - 48y + 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) #

Odpovědět:

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

Vysvětlení:

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

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

# “od rovnice” (2) “my můžeme vyjádřit x v termínech y” # t

# rArrx = 3y-8to (3) #

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

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

# rArry ^ 2 = 9y ^ 2-48ycancel (+64) zrušit (-64) #

# rArr8y ^ 2-48y = 0larrcolor (blue) "factorise" #

# 8y (y-6) = 0 #

# "vyrovnat každý faktor na nulu a vyřešit pro y" #

# 8y = 0rArry = 0 #

# y-6 = 0rArry = 6 #

# "nahradit tyto 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}