Question

已知x=(根号5+1)/2,求(x^8+x^6+x^2+1)/x^4的值.

Answer 1

x=(根号5+1)/2

2x=根号5+1

(2x-1)^2=5

4x^2-4x-4=0

x^2-x-1=0

x^2=x+1

x^4=(x+1)^2=x^2+2x+1=3x+2

x^6=(x^4)*(x^2)=(3x+2)(x+1)=3x2+5x+2=8x+5

x^8=(3x+2)^2=9x2+12x+4=21x+13

原式=(21x+13+8x+5+x+1+1)/(3x+2)=(30x+20)/(3x+2)=10