In Rt△MNC

∫MN = 1，

∴NC= √( 1-x？ ),

① When Rt△AED∽Rt△CMN,

AE/CM=AD/CN，

That is, 1/x=2/√( 1-x? ),

The solution is x= √5/5 or x= -√5/5 (irrelevant, so omitted).

② When Rt△AED∽Rt△CNM,

AE/CN=AD/CM，

That is 1/√( 1-x? )=2/x，

The solution is x= 2√5/5 or -2√5/5 (irrelevant, omitted).

To sum up, when CM= √5/5 or 2√5/5, △AED is similar to a triangle with M, N and C as vertices.

So the answer is: √5/5 or 2 √ 5/5.