以下用 x^n 表示 x的n次方.
= = = = = = = = =
因为 x^2 -x -1=0,
所以 x^2 =x +1.
所以 x^3 =x (x+1)
=x^2 +x
=(x+1)+x
=2x +1,
x^4 =x (2x +1)
=2x^2 +x
=2(x+1) +x
=3x +2,
x^5 =x (3x +2)
=3x^2 +2x
=3(x+1) +2x
=5x +3.
所以 x^5 -5x -3 =0.
= = = = = = = = =
降幂.
x^2 =x+1 是关键.
然后再分别求 x^3,x^4,x^5.
再高的次数也不怕.