Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 230

find all real x,y

find all real x,y such that

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 52,236

Re: find all real x,y

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

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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.

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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

.)