SOLUTION: A positive number is 3 more than twice another number. the difference of their squares is 24. find the two integers. (algebraic solutions only)

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Question 551403: A positive number is 3 more than twice another number. the difference of their squares is 24. find the two integers. (algebraic solutions only)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let the greater number be x and the lesser number be y.
x=2y%2B3, so x%3E2y%3Ey%3E0
Since x%3Ey%3E0, of course x%5E2%3Ey%5E2%3E0.
x%5E2-y%5E2=24
Substituting x=2y%2B3 into x%5E2-y%5E2=24, we get
%282y%2B3%29%5E2-y%5E2=24 --> 4y%5E2%2B12y%2B9-y%5E2=24 --> 3y%5E2%2B12y-15=0 --> y%5E2%2B4y-5=0 --> %28y-1%29%28y%2B5%29=0
The positive solution is y=1. (We ignore solution y=-5 because we know y is positive).
Then x=2y%2B3=2%2A1%2B3=2%2B3=5
So the two integers are 1 and 5.