已知抛物线y=x^2和直线y(m^2-1)x+m^2

y=x^2
y=(m^2-1)x+m^2
联立方程组
x^2=(m^2-1)x+m^2
x^2-(m^2-1)x-m^2=0
两个横坐标为x1,x2
x1+x2=m^2-1
x1x2=-m^2
|x1-x2|=3
两边平方
x1^2+x2^2-2x1x2=9
(x1+x2)^2-4x1x2=9
(m^2-1)^2+4m^2-9=0
(m^2-1)^2+4(m^2-1)-5=0
(m^2-1+5)(m^2-1-1)=0
m^2=-4或者m^2=2
m=√2或者m=-√2

y=x^2
y=(m^2-1)x+m^2
交点：x^2-（m^2-1）x-m^2=0;
(x-m^2)(x+1)=0;
x1-x2=3;
x1=m^2
x2=1
m=+-2