Question

The sum of the reciprocals of 2 consecutive even integers is 7/12. find the numbers

Answer 1

let one integer be x, the consecutive even integer is x+2
reciprocals are $\frac{1}{x} and \frac{1}{x+2}$
$\frac{1}{x} + \frac{1}{x+2}$ =$\frac{7}{12}$

make the denominators the same:
$\frac{x+2}{x(x+2)}$ + $\frac{x}{x(x+2)}$ =$\frac{7}{12}$
$\frac{2x+2}{x(x+2)} = \frac{7}{12}$
12(2x+2)=7x(x+2)
24x+24=7x²+14x
7x²-10x-24=0
the result is not a whole number. Something is not right about this question.