Olympiad Math Question | Algebra Solutions Preparation 2022

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It is simpler to solve by noting that x³+x²+x+1 is a sum of 4 elements of a geometric series with the first element 1 and ratio x. Therefore
0=x³+x²+x+1
=(1-×⁵)/(1-x)
Multiplying by (1-x) gives 1-x⁵=0 --> x=1

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