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)<0), then find S

let x=-1, from f(x)<0, get 2a+b<2, and the area(S) of the cross section between 2a+b<2 and 0 Let x=-2 and -2/1, get the same equation 10a+4b<17, then get S=0;

Observing the equation F(x), we can have
f(x)<0 and f(1/x)<0
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.

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• 回复：回复：回复：Another method -yma16- ♂ (291 bytes) () 04/03/2008 postreply 09:02:18