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Quadruples (a,b,c,d) with abcd=1

Source: Benelux Mathematical Olympiad 2012

April 23, 2012
inequalitiesalgebra proposedalgebra

Problem Statement

Find all quadruples (a,b,c,d)(a,b,c,d) of positive real numbers such that abcd=1,a2012+2012b=2012c+d2012abcd=1,a^{2012}+2012b=2012c+d^{2012} and 2012a+b2012=c2012+2012d2012a+b^{2012}=c^{2012}+2012d.
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