(1) Analysis: Make an image of y=|x2-4x+3| according to the meaning of the question. From the image, we can know that the images of lines y= 1 and y=|x2-4x+3| have three intersections, that is, the equation |x2-4x+3|- 1=0 has three inequalities.

Solution: Make an image of the function y=|x2-4x+3|, as shown in the figure.

According to the image, the image with straight lines y= 1 and y=|x2-4x+3| has three intersections, that is, the equation |x2-4x+3|= 1, that is, the equation |x2-4x+3|- 1=0 has three unequal real roots.

So the answer is: 1.

(2) Analysis: The real number k∈B has no original image in the set A, which means that K should be in the complementary set of the set of corresponding images of all elements in B, so we can find its complementary set according to the known condition that A=B=R and the corresponding rule is F: X→ Y = X2+2x+3.

Solution: When x∈A, under the action of mapping F: A → B.

Corresponding image satisfaction: y=x2+2x+3≥2.

Therefore, if the real number k∈B, there is no original image in set A.

Then k should be satisfied, k < 2.

That is, the range of the real number m that meets the conditions is (-∞, 2).