D is the midpoint of BC side, DB=√2.

De "

= DB" + EB" -2EB*DB*cos45

= 2+(2-x)" - 2√2[(2-x)*(√2/2)]

=2-2x+x "

Let 2-2x+x"=y "

DE = y

EC+ED = x+y

Because x ≥ 0 and y ≥ 0.

So EC+ED≥2√xy

If and only if x=y, the equal sign holds.

X=y is

x=√(2-2x+x”)

The solution is x= 1.

Therefore, when E is the midpoint of AB side, the minimum value of EC+ED is 2.