Question

the sum of the reciprocals of two consecutive integers is -15/56. find the two integers

Answer 1

let the consecutive integers be \(p\) and \(q\) such that \(q = p+1\)

sum of the reciprocals is

\[\frac{1}{p}+\frac{1}{q} = \frac{1}{p} + \frac{1}{p+1} \]Make a common denominator by multiplying the first fraction by \((p+1)/(p+1)\) and the second by \(p/p\). Combine, set equal to -15/56, and solve for \(p\). Use the value of \(p\) to find \(q\).

Answer 2

You'll get two solutions, but one will not be an integer, so it can be ignored.