已知三条直线l1:4x+y-4=0,l2:mx+y=0,l3:2x-3my-4=0交与同一点,则m的值为?

问题描述:

已知三条直线l1:4x+y-4=0,l2:mx+y=0,l3:2x-3my-4=0交与同一点,则m的值为?


由4x+y-4=0
mx+y=0
联立解得交点(4/(4-m),-4m/(4-m))代入l3:2x-3my-4=0得
8/(4-m)+12m²/(4-m)-4=0
整理得m²+m/3-2/3=0
解得m=-1或2/3

答案:m=-1或m=2/3