求分式y=3x^2+6x+5/x^2+2x+2的取值范围

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/15 06:05:18
求分式y=3x^2+6x+5/x^2+2x+2的取值范围求分式y=3x^2+6x+5/x^2+2x+2的取值范围求分式y=3x^2+6x+5/x^2+2x+2的取值范围3x^2+6x+5=3(x^2+

求分式y=3x^2+6x+5/x^2+2x+2的取值范围
求分式y=3x^2+6x+5/x^2+2x+2的取值范围

求分式y=3x^2+6x+5/x^2+2x+2的取值范围
3x^2+6x+5 = 3(x^2+2x+2) -1
所以 y = 3x^2+6x+5/x^2+2x+2 = 3 - 1/(x^2+2x+2)
因为 x^2+2x+2 = (x+1)^2 +1 >=1,
所以 0

y=3x^2+6x+5/x^2+2x+2
=3x^2+6x+6-1/x^2+2x+2
=3+[-1/(x+1)^2+1]
(x+1)^2+1大于等于1
-1+3大于等于3+[-1/(x+1)^2+1]大于0+3
y属于[2,3)