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

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) (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
RELATED QUESTIONS
The difference of two positive numbers is six. Their product is 223 less than the sum of... (answered by josgarithmetic,ikleyn,TeachMath)

the sum of two numbers is 27 and their product is 152, find the... (answered by Alan3354,checkley77)

The square of the difference of two numbers equals the sum of their squares less twice... (answered by solver91311)

Twice the product of two numbers is 56. The sum of their squares is 65. If both numbers... (answered by ewatrrr)

The sum of two numbers is 7, twice their product gives 20. Find the... (answered by ikleyn,Alan3354)

the second of two numbers is 3 less than twice the first. their sum is 18. find the two... (answered by rfer)

the product of two numbers is 162. if their sum is 27, what is their... (answered by mananth)

The sum of two numbers is 9 and the sum of their squares is 261. Find the numbers (answered by ewatrrr)

The product of two numbers is 18 and their sum is 9. Find the numbers. (answered by mananth)