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In the equation 1/j + 1/k = 2/3, both j and k are positive integers. What is the sum of all possible values for k?

 Jan 23, 2021
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1/j + 1/k =  2/3

 

( j + k)   / jk  = 2/3

 

j + k   =  (2/3)jk

 

3 ( j + k)  =  2jk

 

3j + 3k =  2jk

 

3k =  2jk - 3j

 

3k  = j ( 2k - 3)

 

j   =   3k  / ( 2k - 3)

 

 k    j

2    6

3    4

6    2

 

Sum ok all possible values  of  k =   11

 

 

cool cool cool

 Jan 23, 2021

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