设两交点坐标为(x1,y1)(x2,y2),则x1+x2=4,y1+y2=2
x1²-y1²/2=1,x2²-y2²/2=1两式相减得：
(x1-x2)(x1+x2)-(y1-y2)(y1+y2)/2=0
弦的方程斜率k=(y1-y2)/(x1-x2)=2(x1+x2)/(y1+y2)=4
由点斜式得弦的方程：y=4(x-2)+1=4x-7
直线y=4x-7 与双曲线方程联立消去y得：14x²-56x+51=0
x1+x2=4,x1x2=51/14
弦长d=√(1+k²)|x1-x2|
=√17√[(x1+x2)²-4x1x2]
=√17√[16-102/7]
=√1190/7