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#1 2007-12-27 21:44:16

tony123
Member
Registered: 2007-08-03
Posts: 189

find all real x,y

find all real x,y such that

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#2 2007-12-27 21:47:04

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,128

Re: find all real x,y

I can think of only one solution right away.
(0,0) big_smile


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#3 2007-12-28 03:57:33

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: find all real x,y

If you multiply the LHS of the first equation by

, it becomes
. Hence

Because the equations are symmetrical in x and y, you know that the answer must be in the form x = y. Therefore

(x=1 is rejected; it came into the working because I multiplied both sides of the first equation by

.)


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