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Algebra manipulation excercise

Source: 2007 Bulgarian Autumn Math Competition, Problem 9.2

March 17, 2022
algebraSymmetric

Problem Statement

Let aa, bb, cc be real numbers, such that a+b+c=0a+b+c=0 and a4+b4+c4=50a^4+b^4+c^4=50. Determine the value of ab+bc+caab+bc+ca.
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