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#1 2007-12-27 21:44:16
- tony123
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- Registered: 2007-08-03
- Posts: 230
find all real x,y
find all real x,y such that
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#2 2007-12-27 21:47:04
- Jai Ganesh
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- Registered: 2005-06-28
- Posts: 48,428
Re: find all real x,y
I can think of only one solution right away.
(0,0) 
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#3 2007-12-28 03:57:33
- JaneFairfax
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- 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 . HenceBecause 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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