Question

当X等于多少时,(tan^2x-tanx+1)/(tan^2x+tanx+1)有最大值?

Answer 1

令a=tanx,a属于R

y=(a^2-a+1)/(a^2+a+1)

ya^2+ya+y=a^2-a+1

(y-1)a^2+(y+1)a+(y-1)=0

判别式大于等于0

(y+1)^2-4(y-1)^2>=0

(y+1+2y-2)(y+1-2y+2)>=0

(3y-1)(-y+3)>=0

(3y-1)(y-3)