Solution: from the meaning of the question, X 2+KX+ 1 = X 2-X-K = 0.

Then we can get (K+ 1)(X+ 1)=0.

That is K=- 1 or X=- 1.

When K=- 1, the original function is brought in, and it is found that the two functions are the same function, y = x 2-x- 1, which does not meet the meaning of the question and is discarded. Then X=- 1 is brought into the previous equation, and it is known that K=2.

So K=2.