斜率为2的直线L与双曲线C：x2/3-y2/2=1交于A，B两点

y=2x+m
代入双曲线
2x^2-3(2x+m)^2=6
2x^2-12x^2-12mx-3m^2-6=0
10x^2+12mx+(3m^2+6)=0
x1+x2=-12m/10=-6m/5
x1x2=(3m^2+6)/10
(x1-x2)^2=(x1+x2)^2-4x1x2=36m^2/25-2(3m^2+6)/5=(6m^2-60)/25
(y1-y2)^2=[(2x1+m)-(2x2+m)]^2=4(x1-x2)^2=4*(6m^2-60)/25
所以AB^2=(x1-x2)^2+(y1-y2)^2=5*(6m^2-60)/25=4^2
所以(6m^2-60)/5=16
m^2=70/3
m=±√210/3
所以y=2x+√210/3和y=2x-√210/3