Question

对于任意实数x,不等式3x^2+2x+2/x^2+x+1

Answer 1

(3x^2+2x+2)/(x^2+x+1)

=3-(x+1/2+1/2)/[(x+1/2)^2+3/4]

假设y=(x+1/2+1/2)/[(x+1/2)^2+3/4],x+1/2=t

yt^2-t+3y/4-1=0

△1^2-4y(3y/4-1)>=0

3y^1-2y-1