perplexus.info :: Just Math : Just prove it

Just prove it (Posted on 2013-10-20)

Prove that:
If (x+sqrt{1+y^2})*(y+sqrt{1+x^2})=1,
then
x+y=0 .

No Solution Yet Submitted by Ady TZIDON

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Small hint , no spoiler

| Comment 3 of 4 |

Rewrite the equation in the form

y*sqrt{1+y^2}+x*sqrt{1+x^2}=
1-xy-sqrt{1+x^2}*sqrt{1+y^2}

Square both sides, organize & square again

Posted by Ady TZIDON on 2013-10-24 17:26:40

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