SOLUTION: the product of the reciprocals of two consecutive integers is 1/20. Find the integers

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Question 390278: the product of the reciprocals of two consecutive integers is 1/20. Find the integers
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,  

I. Assigning the variable       

Let x and (x+1) represent the two consecutive integers

Question states***

 %281%2Fx%29%281%2F%28x%2B1%29%29+=+1%2F20

 1%2Fx%28x%2B1%29=+1%2F20

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