回复：回复：Another method

S=S(x), S is the area.

f(x)=x^4 + ax^3 - bx^2 + ax + 1

(1) Obiviously,the soltion x0 of f(x)=0 must be less than zero.

(2) My idea is that for a given x, which is less than zero, find the relationship for a and b(from f(x)
let x=-1, from f(x) Let x=-2 and -2/1, get the same equation 10a+4b
Observing the equation F(x), we can have
f(x) are the same.

(3) S(x) has a characteristc, which is
S(x) is a non-increasing fuction in (-1,0) and
S(x) is a non-decreasing fuction in (-infinity,-1),
S(-1) is the maximum, and S(-1)=1/4 is the solution.