# 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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