It is known that when x 1 = a, x2 = b and x3 = c, the quadratic function y= 1/2x? The function values corresponding to +mx are y 1, y2 and y3 respectively. If positive integers A, B and C happen to be three sides of a triangle, the range of m is:

To answer this question, we must clarify two questions:

1. If positive integers A, B and C are just three sides of a triangle, and A

According to the fact that the difference between two sides of a triangle is smaller than the third side, we get:

Because: c>b and a, b and c are positive integers, there must be: c≥b+ 1, so: a >；; c-b≥ 1

That is, the minimum value of a is 2.

2. because when: a

So there is: x =-m/( 1/2) * 2.