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(x+\sqrt{x^2 +1})(y+\sqrt{y^2 +1})= 1 => x+y=0

Source: Norwegian Mathematical Olympiad 1995 - Abel Competition p1b

February 11, 2020
algebra

Problem Statement

Prove that if  (x+x2+1)(y+y2+1)=1(x+\sqrt{x^2 +1})(y+\sqrt{y^2 +1})= 1 for real numbers x,yx,y, then x+y=0x+y = 0.
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