Question

已知双曲线Y=X分之一与直线Y=X-2根号3相交于P(a,b),则a分之一减b分之一=？

Answer 1

1/a-1/b=(b-a)/ab由于P(a,b)为两曲线交点，即满足两个对应方程，因此ab=1,b-a=-2根3，即1/a-1/b=-2根3

追问

谢了

Answer 2

1/x=x-2*Sqr(3)
x^2-2*Sqr(3)x-1=0

the solution is Sqr(3)+2 and Sqr(3)-2

there are two intersection point

1/a=b
1/b=a
1/a-1/b=b-a

so, just subsitute the number back in, there are lots of square roots and mathematics sign.