方法（1）y=ax+1代入双曲线3x2-y2=1得： 3x^2-(ax+1)^2-1=0 ==>3x^2-(ax)^2-2ax-2=0 ==>x^2(a^2-3)+2ax+2=0 ∴x1+x2=-2a/(a^2-3),x1*x2=2/(a^2-3) y1=ax1+1, y2=ax2+1 y1*y2=(ax1+1)(ax2+1)=a^2x1x2+a(x1+x2)+1 ==>2a^2/(a^2-3)+a*(-2a)/(a^2-3)+1 ==>2a^2/(a^2-3)-(2a^2)/(a^2-3)+1 ==>1 ∵OA^2+OB^2=AB^2,(设A（x1,y1),B(x2,y2)) ==>(y2-y1)^2+(x2-x1)^2=(x1-0)^2+(y1-0)^2+(x2-0)^2+(y2-0)^2 ==>x1^2+x2^2+y1^2+y2^2-2x1x2-2y1y2=x1^2+x2^2+y1^2+y2^2 ==>x1x2+y1y2=0 ==>2/(a^2-3)+1=0 ==>a^2=1 ==>a=±1 方法（2）： LOA的斜率是：k1=y1/x1 LOB的斜率是：k2=y2/x2 k1*k2=-1 ==>y1/x1*y2/x2 ==>y1y2/x1x2 ==>1/(2/(a^2-3))=-1 ==>a^2-3=-2 a=±1。
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