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When the sum of the reciprocals of two distinct positive integers is divided by the sum of the two integers, the result is 1/25. What is the sum of the two integers?

 Jan 14, 2019
 #1
avatar+16487 
+1

Can x= y ?  Can they both be 5?

5+5 = 10

 Jan 14, 2019
 #2
avatar+96439 
+2

We have

 

1/a + 1/b

_______   =    1 /25

  a + b

 

[ a + b ] / ab

__________   = 1/ 25

 [ a + b ]

 

[ a + b ] / ab   *     1 / [ a + b ]   =   1 / 25

 

1 / ab   =  1 / 25

 

ab  =   25

 

a = 1  and b = 25

 

And their sum is 26

 

 

cool cool  cool

 Jan 14, 2019

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