y=x²-(m²+4)x-2m²-12
设与x轴的两个交点分别为(x1,0)(x2,0)
∴x1+x2=m²+4
x1x2=-2m²-12
l=12
|x2-x1|=12
∴(x2-x1)²=144
(x1+x2)²-4x1x2=144
(m²+4)²-4(-2m²-12)=144
m^4+8m²+16+8m²+48=144
m^4+16m²-80=0
(m²+20)(m²-4)=0
m²=4
m=2 或m=-2
2、∴(x2-x1)²
=(x1+x2)²-4x1x2
=(m²+4)²-4(-2m²-12)
=m^4+8m²+16+8m²+48
=m^4+16m²+64
=(m²+8)²
∴m²=0时有最小值 最小距离是8