SOLUTION: difference of two positive integer is 5 and their product is 204.find the integers

Question 661573: difference of two positive integer is 5 and their product is 204.find the integers

Answer by ReadingBoosters(3246) (Show Source): You can put this solution on YOUR website!
x-y=5
xy=204
Substitution
(5+y)y=204
5y +y^2-204=0
Rearrange
y^2 + 5y - 204 = 0
(y+ )(y- ) mixed sign due to - 204
Multiples of 204 that will subtract to equal 5: 12,17
(y + 17 )(y - 12 )
y+17=0, so y = -17 NO, must be positive integer
y-12=0, so y = 12 Yes!
x-12=5, so x=5+12=17
Proof
17-12 = 5
17*12 = 204
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