SOLUTION: the sum of the reciprocals of two consecutive even integers is 21/220. find the two integers.

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Question 851631: the sum of the reciprocals of two consecutive even integers is 21/220. find the two integers.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

two consecutive even integers:  x and (x+2)

Question States***

1%2Fx+%2B+1%2F%28x%2B2%29+=+21%2F220

  %282x%2B2%29%2Fx%28x%2B2%29+=+21%2F220    | Cross Multiplying 

   220(2x+2) = 21(x^2 + 2x)

   x^2 - 398x - 440 = 0 

x+=+%28398+%2B-+sqrt%28+195364%29%29%2F%2842%29+

 x+=+%28398+%2B-+sqrt%28+442%29%29%2F%2842%29+   (Tossing out the negative solution for unit measure)

   x = 20, two consecutive even integers are; 20, 22

CHECKING our answer***

1%2F20+%2B+1%2F22+=+42%2F440+=+21%2F220

Wish You the Best in your Studies.