X^2-Y^2/2=1
Y=X+M
两个方程联立
得到x^2-2mx-m^2-2=0
y^2-4my+2m^2-2=0
根据韦达定理
得到x1+x2=2m x1x2=-m^2-2
y1+y2=4m y1y2=2-2m^2
(4√2)^2=(x1-x2)^2+(y1-y2)^2=(x1+x2^2-4x1x2+(y1+y2)^2-4y1y2=32m^2
32=32m^2
m=正负1