已知集合A={(x,y)/y-3/x-2=a+1},集合B={(x,y)/(a^2-1)x+(a-1)y=30},若A并B=空集,求实数a的值

Question

已知集合A={(x,y)/ y-3/x-2=a+1},集合B={(x,y)/ (a^2-1)x+(a-1)y=30},若A并B=空集,求实数a的值

Answer 1

A交B为空 则联立方程组的解集为空,解此方程组 (y-3)/(x-2)=a+1 y=(a+1)x-2a+1 代入(a^2-1)x+(a-1)y=9 (a^2-1)x+(a-1)((a+1)x-2a+1)=9 (a^2-1)x+(a^2-1)x=(a-1)(2a-1)+9 则a^2-1=0 且(a-1)(2a-1)+9不为0 a=1或a=-1 或...