Question

已知x=(根号5+1)/2求x三次方/x三次方+x+1

Answer 1

已知x=(根号5+1)/2

2x-1=根号5

平方得 4x²-4x+1=5

即x²=x+1

所以x三次方/(x三次方+x+1)

=x(x+1)/[x(x+1)+x+1]

=x/(x+1)

=1/(1+1/x)

=1/[1+2/(√5+1)]

=(√5+1)/(3+√5)

=(1+√5)(3-√5)/(9-5)

=(2√5-2)/4

=(√5-1)/2