SOLUTION: the product of two consecutive positive integers is 52 more than 8 times the larger integer. Find the integers

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Question 962751: the product of two consecutive positive integers is 52 more than 8 times the larger integer. Find the integers
Answer by hkwu(60) About Me  (Show Source):
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Let a, b be the two integers. Without loss of generality, let a be the larger integer. Then
a%2Ab=8a%2B52
a%2Ab-8a-52=0
and
a=b%2B1
since the two integers are consecutive and a is larger.
%28b%2B1%29%2Ab-8%28b%2B1%29-52=0
b%5E2%2Bb-8b-8-52=0
b%5E2-7b-60=0
%28b-12%29%28b%2B5%29=0
Thus b = 12 or b = -5, but the integers are positive so b must be 12. We conclude that a = 13.
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