SOLUTION: One positive integer is 5 more than twice another. The sum of their squares is 185 . Find the integers.

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Question 946914: One positive integer is 5 more than twice another. The sum of their squares is 185 . Find the integers.
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
x = larger integer
y = smaller integer

x = 2y + 5
x^2 + y^2 = 185

Substitute the first equation into the second equation.

(2y - 5)^2 + y^2 = 185
(4y^2 - 20y + 25) + y^2 = 185
5y^2 - 20y - 160 = 0
y^2 - 4y - 32 = 0
(y + 8)(y - 4) = 0

The integers are positive, so y = 4.

The integers are x = 13 or y = 4.