SOLUTION: The sum of two numbers is 27. The sum of their squares is 9 less than twice their product. Find the two numbers.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: The sum of two numbers is 27. The sum of their squares is 9 less than twice their product. Find the two numbers.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 655569: The sum of two numbers is 27. The sum of their squares is 9 less than twice their product. Find the two numbers.
Answer by MathDazed(34) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + y^2 -9 = 2xy (i)
x + y = 27 (ii)
Making x the subject in equation (ii) x = 27 - y
substitute x = 27-y into equation (i)
(27-y)^2 + y^2 - 9 = 2(27-y)y
729 - 27y -27y + y^2 + y^2 - 9 = 54y - 2y^2
Collect like terms and equate to zero
729 -9 - 27y -27y - 54y + 2y^2 +2y^2 = 0
4y^2 - 108y +720 = 0
Divide by 4
y^2 - 27y + 180 = 0
(y -12)(y-15) = 0
y=12; y=15
When y = 12; x = 15
When y = 15; x = 12