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How many ordered pairs of positive integers (x,y) satisfy the equation x=4-x over y^2-x?

Guest Jan 9, 2018
 #1
avatar+88898 
+2

x  =   (4 - x) /  ( y^2  - x)     rearrange as

 

y^2 - x  =  (4 - x) /  x

 

y^2  =  4/x - 1  +  x

 

y^2  =  ( x - 1)  +  4/x

 

Note that   ( x - 1)  will be an integer for all integer values for x

 

But     4/x     will only be an integer when   x  = 1, 2  or 4

 

When   x  =  1,  y   =  2

When x  =  2, y  = √3

When x  =  4, y   = 2

 

However....(4,2)  produces a denominator = 0 in the original equation....so....this answer must be rejected...!!!

 

So.....(1,2)  is the  only correct answer

 

EDIT :  Thanks to hectictar for spotting my preious error  !!!! 

 

 

cool cool cool   

CPhill  Jan 9, 2018
edited by CPhill  Jan 10, 2018

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