Analysis: Inferring the isosceles right triangle of △BDE from the equal corresponding angle of similar triangles; E(a, 3/a) and D(b, 3/b) can be set according to the coordinate characteristics of points on the inverse proportional function image, and AB = 3； is obtained from the properties of isosceles right triangle; Finally, we can get it by substituting the value of a into the analytical formula of straight line AD.

Answer:

Solution: As shown in the figure, the intersection point D is DF⊥BC of point F,

Bca = 90, AC=BC=2√2, the image of inverse proportional function y = 3/x (x > 0) intersects AB and BC at points D and E, ∴∠BAC =∠ABC = 45°, which can be set as E.

∴C(a,0),B(a,2√2),A(a-2√2,0)，

∴ The analytical formula for finding straight line AB is: y = x+2 √ 2-a. 。

∫△BDE∽△BCA，

∴△BDE is also an isosceles right triangle,

∴DF=EF，

∴a-b=3/b-3/a, namely AB = 3.

Point d is on the straight line AB,

∴(3/b)=b+2√2-a, that is, 2A 2-(2 √ 2) A-3 = 0, and the solution is a=(3/2)√2.

The coordinates of point E are ((3/2)√2, √2).

So the answer is: ((3/2)√2, √2).