已知双曲线y=3/x和直线y=kx+2相交于点A(X1,Y1)和点B(X2,Y2),且X1*X1+X2*X2=10,求k的值?

问题描述:

已知双曲线y=3/x和直线y=kx+2相交于点A(X1,Y1)和点B(X2,Y2),且X1*X1+X2*X2=10,求k的值?

y=3/x,y=kx+2
(kx+2)x=3
kx^2+2x-3=0
x1+x2=-2/k,x1x2=-3/k
X1*X1+X2*X2=10
(x1+x2)^2-2x1x2=10
4/k^2+6/k=10
5k^2-3k-2=0
k=-2/5,或k=3