MathDB
a+b+c+d=2 and ab+bc+cd+da+ac+bd = 0, find min, max of abcd

Source: Balkan BMO Shortlist 2016 A5

July 30, 2019
algebrasystem of equationsinequalitiesminimummaximumIMO Shortlist

Problem Statement

Let a,b,ca, b,c and dd be real numbers such that a+b+c+d=2a + b + c + d = 2 and ab+bc+cd+da+ac+bd=0ab + bc + cd + da + ac + bd = 0. Find the minimum value and the maximum value of the product abcdabcd.
Back to ProblemsView on AoPS