Question

如果方程x2+(m-1)2+m2-2=0的两个实数根一个小于-1,一个大于1,那么实数m的取值范围

Answer 1

Δ>0
(m-1)^2-4(m^2-2)>0
-3m^2-2m+9>0
3m^2+2m-9<0
3(m+1/3)^2-28/3<0
(-1-2√7)/3<m<(-1+2√7)/3 ①
f(x)=x^2+(m-1)x+m^2-2
f(-1)<0
1+(m-1)*(-1)+m^2-2<0
m^2-m-1<0
(m-1/2)^2-5/4<0
(1-√5)/2<m<(1+√5)/2 ②
f(1)<0
1+(m-1)*1+m^2-2<0
m^2+m-3<0
(m+1/2)^2-13/4<0
(1-√13)/2<m<(1+√13)/2 ③
m的取值范围为①②③的交集：(1-√5)/2<m<(-1+2√7)/3

Answer 2

根据题意，需同时满足以下三个条件：
①判别式△>0
②f(-1)<0
③f(1)>0
然后你自己算一下就好啦~~三个结果取一下交集