g(a,b)=(x+ 1/x)a+b+(x^2+ 1/x^2)=0

This is a straight line, and the square of the point (0,0) and the distance between it is also (A 2+B 2):

(x^2+ 1/x^2)^2/((x+ 1/x)^2+ 1)

Let c = (x 2+1/x 2+3), and the above formula is

(c-3)^2/c(c & gt； =5)

=(√c-3/√c)^2

Therefore, the smaller c is, the larger the above formula is, so when c=5, the above formula =4/5 is the smallest.

Appendix: the distance between ax+by+c=0 and ax+by+d=0 is:

|c-d|/√(a^2+b^2)