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Given positive integers x and y such that \(x\neq y\) and \(\frac{1}{x} + \frac{1}{y} = \frac{1}{18}\), what is the smallest possible value for \(x+y\)?

 Aug 25, 2018
 #3
avatar+101796 
+2

1/x  +  1/y  =  1/18

 

18 [ x + y]   =  xy

 

18  = xy / [ x + y ]

 

Let  x  = 45  and y  = 30 

 

18  = 45 * 30 / [ 75 ]  =   15 * 3 * 15 * 2  / [ 15 * 5]  =  90 / 5

 

So

 

x + y   =  45 + 30   =  75

 

 

cool cool cool

 Aug 25, 2018
 #4
avatar+814 
+4

Thank you for a nice explanation, CPhill!

mathtoo  Aug 25, 2018

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