x³ $$-$$ 2x² + 2x $$-$$ 1 = 0

x = 1 satisfying the equation

$$ \therefore $$ x $$-$$ 1 is factor of

x³ $$-$$ 2x² + 2x $$-$$ 1

= (x $$-$$ 1) (x² $$-$$ x + 1) = 0

x = 1, $${{1 + i\sqrt 3 } \over 2},{{1 - i\sqrt 3 } \over 2}$$

x = 1, $$-$$ $$\omega$$², $$-$$$$\omega$$

Sum of 162^th power of roots

= (1)¹⁶² + ($$-$$$$\omega$$²)¹⁶² + ($$-$$$$\omega$$)¹⁶²

= 1 + ($$\omega$$)³²⁴ + ($$\omega$$)¹⁶²

= 1 + 1 + 1 = 3