Question

已知一次函数Y=—根号3/3X+b与反比例函数Y=K/X在第一象限内交于B、C两点,与Y轴交于A点,且AB乘AC=4,求

Answer 1

A(0,b),一次函数图像斜率k=—根号3/3,设B、C横坐标分别为x1,x2

AB=根号（1+k^2)|x1-0|,AC=根号（1+k^2)|x2-0|

AB*AC=根号(1+k^2)|x1|*根号（1+k^2)|x2|=(1+k^2)x1x2=(1+1/3)x1x2=(4/3)x1x2=4,

x1x2=3,把Y=K/X代入Y=—根号3/3X+b得根号3/3X^2-bx+K=0,

x1x2=(根号3)K=3,K=根号3