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What is the only solution to 1/x + 1/y = 1/123 where x < y?

 Oct 20, 2024
 #1
avatar+1237 
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What is the only solution to 1/x + 1/y = 1/123 where x < y?    

 

You could go for 3 / (3)(123) which would be    

written as 1 / 369 + 2 / 369 = 3 / 369 = 1 / 123     

but I don't guarantee that it's the only solution.   

.   

 Oct 20, 2024
 #3
avatar+1237 
0

 

I made a conversion mentally that I now feel I should have shown explicitly.  

 

The problem asks for 1/x + 1/y = 1/123         with x < y    

 

I submitted 1/369 + 2/369 = 3/369 = 1/123  

 

For clarity, there should have been a step before that.    

 

                  1/369 + 1/184.5    

 

Stated thus, the x and y positions are reversed.    

Pedantically, I admit I should not have done that.   

I just thought the equation looked nicer as 1, 2, 3. 

 

x = 184.5 and y = 369     note that x < y   

 

check answer       

 

1/x        + 1/y       =  1/123    

1/184.5 + 1/369  =?  1/123      

2/369    + 1/369  =  3/369  =  1/123       True    

.   

Bosco  Oct 21, 2024
edited by Bosco  Oct 22, 2024

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