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Regional Olympiad - FBH 2010 Grade 9 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2010

September 27, 2018

algebraBosnia

Problem Statement

For real numbers

a

b

c

and

d

holds:

a+b+c+d=0

a^3+b^3+c^3+d^3=0

Prove that sum of some two numbers

a

b

c

and

d

is equal to zero