SOLUTION: the reciprocal of theproduct of two consecutive integers is 1/73. find the two integers

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Question 894080: the reciprocal of theproduct of two consecutive integers is 1/73. find the two integers
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
n and n+1 are the consecutive integers.

1%2F%28n%28n%2B1%29%29=1%2F73.

Built this way:
The product of the integers, n%28n%2B1%29.
The reciprocal of the product, 1%2F%28n%28n%2B1%29%29.

That is 1%2F73,
1%2F%28n%28n%2B1%29%29=1%2F73.

This is equivalent to n%5E2%2Bn=73, which MUST be factorable using only integers. 73 is a PRIME number.
Discriminant of the equation, n%5E2%2Bn-73=0.
1%5E2%2B4%2A73=293, which is NOT a perfect square. This means neither n nor n+1 is an integers.

The question or problem description is wrong.