If α, β are the roots of x² - x + 1 = 0, then α²⁰⁰⁹ + β²⁰⁰⁹ =
Q1. If α, β are the roots of x² - x + 1 = 0, then α²⁰⁰⁹ + β²⁰⁰⁹ =
Answer: -1
Explanation: The roots are complex cube roots of unity, so α³ = 1 and β³ = 1, hence α²⁰⁰⁹ + β²⁰⁰⁹ = (α³)⁶⁷³ + (β³)⁶⁷³ = -1.