Question

若不等式x-a/x2+x+1＞x-b/x2-x+1的解为1/2＞x＞1,求a,b的值

Answer 1

x^2+x+1=(x+1/2)^2+3/4>0

x^2-x+1=(x-1/2)^2+3/4>0

两个分母都大于0

所以两边乘以(x^2+x+1)(x^2-x+1)

(x-a)(x^2-x+1)>(x-b)(x^2+x+1)

x^3-(a+1)x^2+(a+1)x-a>x^3+(1-b)x^2+(1-b)x-b

-(a+1)x^2+(a+1)x-a>(1-b)x^2+(1-b)x-b

(1-b+a+1)x+(1-b-a-1)x+a-