Question 278332
The product of a positive even integer and the reciprocal of the next larger positive even integer equals the reciprocal of the first integer. Find the integer.

Let one number be x

the other number will be x+2

reciprocal of this number = 1/ x+2

x* 1/ x+2 = 1/x

x/ x+2 =1/x

x^2=x+2

x^2-x-2=0

x^2-2x+x-2=0

x(x-2)+1(x-2)=0

(x+1)(x-2)=0

x=-1 or x=2

Answer 2