SOLUTION: find two consecutive positive integers such that the square of the smaller integer added to six times the larger integer is equal to 61

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Those integers are n and n+1
where n^2+6(n+1)=61
n^2+6n-55 = 0
(n+11)(n-5) = 0
n = -11 or n = 5
Then n = 5 and n+1 = 6
Answer: 5 and 6
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