+0  
 
+1
28
1
avatar

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

 
Guest Jan 9, 2018
Sort: 

1+0 Answers

 #1
avatar+80791 
+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

31 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details