SOLUTION: hey there thanks ,the question is- the difference between two numbers is 4 and the sum of their squares is80 less than three times their product. Find the numbers thanks again.

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Question 222358: hey there thanks ,the question is-
the difference between two numbers is 4 and the sum of their squares is80 less than three times their product. Find the numbers
thanks again.
xx

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
the difference between two numbers is 4
x - y = 4
or
x = (y + 4)
:
"the sum of their squares is 80 less than three times their product."
x^2 + y^2 = 3xy - 80
x^2 - 3xy + y^2 = -80
;
replace x with (y+4)
(y+4)^2 - 3y(y+4) + y^2 = -80
y^2 + 8y + 16 - 3y^2 - 12y + y^2 = -80
:
Combine like terms
y^2 + y^2 - 3y^2 + 8y - 12y + 16 + 80 = 0
:
-y^2 - 4y + 96 = 0
:
Multiply by -1
y^2 + 4y - 96 = 0
:
Factor:
(y+12)(y-8) = 0
:
Positive solution
y = 8
find x
x = 8 + 4
x = 12
:
Check
12^2 + 8^2 = 3*12*8 - 80
144 + 64 = 288 - 80
208 = 208
:
:
How about the solution y = -12?
then
x = -12 - 4
x = -16
:
-16^2 + -12^2 = 3*-16*-12 - 80
256 + 144 = 576 - 80
not a solution