已知x^2-(3m+2)x+2(m+6)=0的两个实根都大于1,求实数m的取值范围思路：△》0,f(1)>0,-b/2a>1不过老是算不到2

Question

已知x^2-(3m+2)x+2(m+6)=0的两个实根都大于1,求实数m的取值范围
思路：
△》0,f(1)>0,-b/2a>1
不过老是算不到2

Answer 1

x^2-(3m+2)x+2(m+6)=0
(3m+2)²-8(m+6)≥0
9m²+12m+4-8m-48≥0
9m²+4m-44≥0
(m-2)(9m+22)≥0
m≥2 或者m≤-22/9
(3m+2)/2>1
3m>0
m>0
1-(3m+2)+2(m+6)>0
1-3m-2+2m+12>0
11-m>0
m