若直线Y=KX（K不为0）和双曲线Y=-2/X交于A（X1,Y1）B(X2,Y2)两点,求3X1Y2-5X2Y1的值

若直线Y=KX（K不为0）和双曲线Y=-2/X交于A（X1,Y1）B(X2,Y2)两点,求3X1Y2-5X2Y1的值
若直线Y=KX（K不为0）和双曲线Y=-2/X交于A（X1,Y1）B(X2,Y2)两点,求3X1Y2-5X2Y1的值

若直线Y=KX（K不为0）和双曲线Y=-2/X交于A（X1,Y1）B(X2,Y2)两点,求3X1Y2-5X2Y1的值
AB代入
y1=kx1
y2=kx2
xy=-2
所以x1y1=-2
x2y2=-2
所以x1x2y1y2=4
x1x2*kx1*kx2=4
(kx1x2)²=4
kx1x2=±2
所以3x1y2-5x2y1
=3x1*kx2-5x2*kx1
=-2kx1x2
=-4或4