Question

已知x^2+x=-1 你能求x^2013+x^2012+x^2011+x^2010+x^2009+…+x^4+x^3+x

Answer 1

∵ x²+x+1 = 0

x^2013+x^2012+x^2011+…+x^3+x²+x+1

= (x²+x+1)x^2011 + (x²+x+1)x^2008 + (x²+x+1)x^2005 +…… + (x²+x+1)x^4 + (x²+x+1)x +1

= 1