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Just prove it (Posted on 2013-10-20) Difficulty: 2 of 5
Prove that:
If (x+sqrt{1+y^2})*(y+sqrt{1+x^2})=1,
x+y=0 .

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts Musing on possible lines of attack | Comment 2 of 4 |
As Steve pointed out y=-x does always work.  What remains is to show that for any given x, y=-x is the only thing that works.

For many values of x, the function of y is strictly increasing, but I'm finding this hard to prove.  And for some values it isn't.

Another line of reasoning is that because we are looking for a product that is positive it is clear that if x is positive, y must be negative.  Unfortunately a negative x does not imply a positive y.

  Posted by Jer on 2013-10-23 08:55:08
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