A Great Math Olympiad Problem that Looks Complicated / Germany

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[@SrisailamNavuluri]

xy=32=1×32=2×16=4×8
Here 4+8=12
(x,y)=(4,8) or (8,4)

[@prollysine]

x=32/y , --> , y^2 - 12y + 32=0 , --> , y^2-8y -4y+32=0 , (y-8)(y-4)=0 , y= 8 , 4 , x=12-y , case 1 , y=8 , x=12-8 , x=4 ,
+1 -8 case 2 , y=4 , x=12-4 , x=8 ,
-4 +32=0 , solu , (x , y) , (4 , 8) , (8 , 4) , test , x*y=32 , 4*8=8*4 , --> , 32 , OK ,

[@ricnyc2759]

x = 8
y = 4
8 + 4 = 12
8 x 4 = 32