Application of Equations #1

Algebra Level pending

Three complex numbers \(\alpha,\beta,\gamma\) satisfy below three equations.

  • \(\alpha+\beta+\gamma=1\)

  • \(\alpha^2+\beta^2+\gamma^2=3\)

  • \(\alpha\beta\gamma=1\)

Find the value of \(\alpha^{10}-\alpha^9-\alpha^8+\beta^{10}-\beta^9-\beta^8+\gamma^{10}-\gamma^9-\gamma^8\).

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