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Su Ke Edition Ninth Grade Mathematics Volume II
Solution: Transform the equation into1x-1= (x-1) 2,

Let y 1= 1x- 1, y2=(x- 1)2, and draw the images of two functions in the coordinate system as shown:

It can be seen that the two functions have an intersection (1, 0).

So the equation x2-2x= 1x-2 has a real root.

So choose C.