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The sum of $162^{\text{th}}$ power of the roots of the equation $x^3 - 2x^2 + 2x - 1 = 0$ is
$x^3 - 2x^2 + 2x - 1 = (x-1)(x^2-x+1) = 0$. Roots: $1, \omega, \omega^2$ (cube roots of unity, where $\omega = e^{i2\pi/3}$). Sum $= 1^{162} + \omega^{162} + \omega^{324} = 1 + 1 + 1 = 3$ (since $162 = 54 \times 3$).
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