Question 390278
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Hi,  
I. Assigning the variable       
Let x and (x+1) represent the two consecutive integers
Question states***
 {{{(1/x)(1/(x+1)) = 1/20}}}
 {{{1/x(x+1)= 1/20}}}
Cross Multitply to solve for x 
 x(x+1) = 20
 x^2 + x - 20 = 0
factoring
   (x+5)(x-4)=0 Note:SUM of the inner product(5x) and the outer product(-4x) = x
   (x+5)= 0  x = -5  the Two consecutive integers are -5,-4
or (x-4)=0   x =  4  the Two consecutive integers are 4,5

CHECKING our Answer(s)***
 -1/5*-1/4 = 1/20  and 1/4*1/5 = 1/20