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Regional Olympiad - FBH 2011 Grade 12 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2011

September 27, 2018
algebraInequalityinequalities proposed

Problem Statement

If for real numbers xx and yy holds (x+1+y2)(y+1+x2)=1\left(x+\sqrt{1+y^2}\right)\left(y+\sqrt{1+x^2}\right)=1 prove that (x+1+x2)(y+1+y2)=1\left(x+\sqrt{1+x^2}\right)\left(y+\sqrt{1+y^2}\right)=1
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