把 y=2x-3代入双曲线方程得
x^2/2-(2x-3)^2=1
x^2-2(4x^2-12x+9)=2
x^2-8x^2+24x-18=2
7x^2-24x+20=0
x1+x2=24/7 x1x2=20/7
(x1-x2)^2=(x1+x2)^2-4x1x2=24^2/7^2-20*4/7=(576-560)/47=16/49 (假设x1>x2,便于计算)
x1-x2=4/7
y1-y2=2x1-3-(2x2-3)=2(x1-x2)=2*4/7=8/7
所以
|AB|=√(x1-x2)^2+(y1-y2)^2=√(4/7)^2+(8/7)^2=4√5/7