Question

x=(（根号5）-1)除以2,则x^4+x^2+2x+1=,我知道是5-根号5

Answer 1

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

x^4=(（根号5）-1)/2)^4=(56-24根号5)/16,

(x+1)^2=(（根号5）+1)/2)^2=(6+2根号5)/4

x^4+x^2+2x+1=x^4+(x+1)^2=5-根号5