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ab + bc + ca =? if a + b + c = 0 and a^4 + b^4 + c^4 = 128

Source: 2019 Irish Mathematical Olympiad paper 2 p7

October 5, 2020
algebra

Problem Statement

Three non-zero real numbers a,b,ca, b, c satisfy a+b+c=0a + b + c = 0 and a4+b4+c4=128a^4 + b^4 + c^4 = 128. Determine all possible values of ab+bc+caab + bc + ca.
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