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For any 8 certain points, 4 terms dependent on these are not al positive

Source: Romanian NO, Grade IX, P.2

October 2, 2019
algebra

Problem Statement

Show that for any four positive real numbers a,b,c,d a,b,c,d and four negative real numbers e,f,g,h, e,f,g,h, the terms ae+bc,ef+cg,fd+gh,da+hb ae+bc,ef+cg,fd+gh,da+hb are not all positive.
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