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

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) (Show Source): You can put this solution on YOUR website!
Let a, b be the two integers. Without loss of generality, let a be the larger integer. Then

and

since the two integers are consecutive and a is larger.

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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