Math olympiad Question | Algebra Problem | If 𝑥^2+𝑥+1=0 then 𝑥^2023+𝑥^2024+2024 = ?

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Math olympiad Question | Algebra Problem | If 𝑥^2+𝑥+1=0 then 𝑥^2023+𝑥^2024+=2024 ?

This video discusses a famous problem on algebra taken from an olympiad. A problem on algebraic identities.

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There is another easier solving!
x^k + x^(k+1) + x^(k+2) = 0
for k=
See that sum:
1 + x + x^2 + x^3 + x^4 + . . . + x^2023 + x^2024 = 0
cause then are 2025 = 3*675 numbers in sum.
I make parenthesises:
1 + (x + x^2 + x^3) + (x^4 + x^5 + x^6) + . . . +(x^2020 + x^2021 +x^2022) + x^2023 + x^2024 = 0
The parentesises are 0. So
1 + x^2023 + x^2024 = 0
Give plus 2023 then
2024 + x^2023 + x^2024 = 2023

peterzsiros