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How many ordered pairs of positive integers satisfy the equation, 1/x + 1/y = 1/6 with x

 Jan 31, 2019
 #1
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1/x + 1/y = 1/6

 

[ x + y ] / xy =  1 / 6

 

xy / [ x + y ]  = 6

 

xy =  6 [ x + y]

 

xy = 6x + 6y

 

xy - 6y  = 6x

 

y ( x - 6) = 6x

 

y =  6x / (x - 6)

 

When  x = 7    y = 42

When x = 8 , y = 24

When x = 9, y = 18

Whex = 10, y = 15

When x = 12, y = 12

 

So....these are the solutions...........note..... x and y are abrbitrary......so these answers can be "reversed" for x and y

 

 

 

cool cool cool

 Jan 31, 2019

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