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abcd=4, a^2+b^2+c^2+d^2=10, maximize (a+c)(b+d)

Source: 2012 Czech and Slovak, P6

April 12, 2013
inequalitiesinequalities proposed

Problem Statement

Let a,b,c,da,b,c,d be positive real numbers such that abcd=4abcd=4 and a2+b2+c2+d2=10.a^2+b^2+c^2+d^2=10. Find the maximum possible value of ab+bc+cd+daab+bc+cd+da.
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