Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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

find all real x,y such that

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,063

I can think of only one solution right away.

(0,0)

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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

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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