Math plz help 已知a+1/a=1,求a^2015+1/a^2015的值.?

因為 a + 1/a = 1
所以 a² + 2 + 1/a² = 1
即 a² + 1/a² = -1 ⋯⋯⋯⋯ ①
又 a + 1/a = 1
==> a² - a + 1 = 0
==> (a + 1)(a² - a + 1) = 0
==> a³ + 1 = 0
==> a³ = -1 ⋯⋯⋯⋯⋯⋯ ②
所以
a²⁰¹⁵ + 1/a²⁰¹⁵
= a²[(a³)⁶⁷¹] + 1/a²[(a³)⁶⁷¹]
= a²[(-1)⁶⁷¹] + 1/a²[(-1)⁶⁷¹] ⋯⋯ (從 ② 得知 a³ = -1)
= -a² - 1/a²
= -(a² + 1/a²)
= -(-1) ⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯ (從 ① 得知 a² + 1/a² = -1)
= 1

Sol
a+1/a=1
a^2+1=a
a^2－a+1=0
(a+1)(a^2－a+1)=0
a^3+1=0
a^3=－1
a^2015=a^2013*a^2=－a^2
a^2015+1/a^2015
=－a^2－1/a^2
=(－a+1)/a^2
=－a^2/a^2
=－1