SOLUTION: The larger of two positive integers is three more than the smaller. If twice the square of the smaller integer is increased by three times the larger integer, the result is 74. Fin

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Question 741915: The larger of two positive integers is three more than the smaller. If twice the square of the smaller integer is increased by three times the larger integer, the result is 74. Find the integers.
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
x = y + 3
2y^2 + 3x = 74

Substitute x = y + 3 into the second equation.

2y^2 + 3(y + 3) = 74
2y^2 + 3y + 9 = 74
2y^2 + 3y - 65 = 0
(y - 5)(2y + 13) = 0
y = 5, y = -13/2

y is a positive integer, so the integers are (x, y) = (8, 5)