Solution: 1-x|x|-x=0.

( 1)x & gt； 0

x^2+x- 1=0

X=(- 1+ radical number 5)/2 or x=(- 1- radical number 5)/2.

(2)x & lt； 0

x^2-x+ 1=0

X=( 1+ radical number 5)/2 or x=( 1- radical number 5)/2.

Substituting 1/x+|x| respectively gives the root number 5, 1, root number 5, 1.

So choose D.

There is also a whole replacement method. I can't remember today. If you have any questions, just say so.