Solution: According to Vieta's theorem, in the equation AX 2+BX+C = 0, A ≠ 0, two x 1 x2 have the following relations with A, B and C.

X 1+x2= -b/a, x1* x2 = c/a. Comparing with the equation of this problem, X 1+X2 = 2-m, X 1 * X2 = m-3.

So we have x12+x2 2 = (x1+x2) 2-2x1x 2 = (2-m) 2-2 (m-3), which is simplified as: m 2-6m+/kloc.

It is to ask for the minimum value of this formula. Short formulas like this are generally simplified to the form of square+real number.

So m2-6m+1 0 = (m2-6m+3 2)+1= (m-3) 2+1,and when m=3, there is a minimum value1.