Question

已知集合A={2,4,x^2-5x+9},B={3,x^2+ax+a},C={1,x^2+(a+1)x-3},其中a,x

Answer 1

解由题意知 x+ax+a=1 ① x+(a+1)x-3=3 所以x+ax=1-a x+ax=6-x 解得a=x-5代入① x+(x-5)x+x-5=1 即x-2x-3=0 (x-3)(x+1)=0 x=3,a=-2 or x=-1,a=-6 当x=3,a=-2时,集合A=｛2,4,3｝,B=C=｛3,1｝ 当x=-1,a=-6时,集合A=｛2,4,15｝,B=C=｛3,1｝ 答：x=3,a=-2 or x=-1,a=-6即为所求.