Ano ang mga posibleng halaga (s) ng x at y kung y ^ 2 = x ^ 2-64 at 3y = x + 8 ??

Sagot:

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

Paliwanag:

# 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 at y = 0 #:

# x = 0 - 8 #

# = -8#

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

# x = 3 xx 6 - 8 #

# x = 10 #

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

Sagot:

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

Paliwanag:

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

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

# "mula sa equation" (2) "maaari naming ipahayag ang x sa mga tuntunin ng y" #

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

# "kapalit" x = 3y-8 "sa equation" (1) #

# rArry ^ 2 = (3y-8) ^ 2-64larrcolor (asul) "palawakin" (3y-8) ^ 2 #

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

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

# 8y (y-6) = 0 #

# "ihambing ang bawat salik sa zero at lutasin ang y" #

# 8y = 0rArry = 0 #

# y-6 = 0rArry = 6 #

# "palitan ang mga halagang ito sa equation" (3) #

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

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

(x-8) ^ 2 + (y-0) ^ 2-0.04) ((x-10) ^ 2+ (y-6) ^ 2-0.04) = 0 -20, 20, -10, 10}