Diketahui x + x⁻¹ = 1. Berapa nilai dari x⁷ + x⁻⁷ ?

Mapel : Matematika
Tingkat : Olimpiade
Bab : Aljabar

Pembahasan :
x + 1/x = 1

x² + (1/x²) = [x + (1/x)]² - 2
= 1² - 2 = -1

x^4 + 1/x^4
= [x² + (1/x²)] - 2
= (-1)² - 2
= 1 - 2 = -1

[x^4 + (1/x^4)] . [x² + (1/x²)] . [x + (1/x)
= (-1)(-1)( 1)
= 1