MathDB
One of a,b,c,d is not greater than -1

Source: Baltic Way 2002

November 13, 2010
inequalities proposedinequalities

Problem Statement

Let a,b,c,da,b,c,d be real numbers such that a+b+c+d=−2a+b+c+d=-2 ab+ac+ad+bc+bd+cd=0ab+ac+ad+bc+bd+cd=0 Prove that at least one of the numbers a,b,c,da,b,c,d is not greater than −1-1.
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