Unless there's some information we're missing here, you are correct when you say that and are the only stationary points.
x + 1/x
dy/dx =
Solve for x
1/x^2 = -1
x^2 = -1 * -1
x = + or - sqrt 1
Is this correct? If so, I don't see how it works, as the answer only has a +1 as a stationary point coordinate. The other x is a 5, but I don't see how you'd get that.