SOLUTION: please help me in this question: the sum of the reciprocal of two consecutive integers is 17/12.find the integers

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Trying the numbers 1 and 2 gives a sum of the reciprocals of
Trying the numbers 2 and 3 gives a sum of the reciprocals of
If the sum is then the first number must be slightly less than 1 and 2.
If the sum is then the first number must be slightly greater than 1 and 2.
Solving the problem using the quadratic formula and gives a result of 0.937117256.
Solving the problem using the quadratic formula and gives a result of 1.070908304.
I am doubtful that this problem has an integer solution.