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Algebraic ineq in triangle

Source:

January 5, 2006
geometryperimeterinequalitiestriangle inequality

Problem Statement

If a,b,ca,b,c are the sides of a triangle whose perimeter is equal to 2 then prove that: a) abc+2827≥ab+bc+acabc+\frac{28}{27}\geq ab+bc+ac; b) abc+1<ab+bc+acabc+1<ab+bc+ac See also http://www.mathlinks.ro/Forum/viewtopic.php?t=47939&view=next (problem 1) :)
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