x^2-x+1=0,求x^10+x^20+x^30=?用初中知识,不要求虚数值带入.RT.回一楼：delta小于零。_数学解答

x^2-x+1=0,求x^10+x^20+x^30=?用初中知识,不要求虚数值带入.
RT.
回一楼：delta小于零。

人气：147 ℃　时间：2020-09-30 08:58:20

解答

x²=x-1
x^10=(x²)^5
=(x-1)^5
=(x-1)²(x-1)²(x-1)
=(x²-2x+1)(x²-2x+1)(x-1)
=(x-1-2x+1)(x-1-2x+1)(x-1)
=(-x)(-x)(x-1)
=x²(x-1)
=(x-1)(x-1)
=x²-2x+1
=x-1-2x+1
=-x
x^20=(x^10)²=x²
x^30=(x^10)^3=-x^3
原式=-x^3+x²-x
=-x(x²-x+1)
=0