设集合A={x丨x^2+x-1=0},B={x丨ax+1=0},若B包含于A,则a=

Question

设集合A={x丨x^2+x-1=0},B={x丨ax+1=0},若B包含于A,则a=

Answer 1

当a=0时,
B是空集,
当a≠0时,
x=1/a
1/a∈A
1/a²+1/a-1=0
1+a-a²=0
a²-a-1=0
a=(1±√5)/2
所以
a∈{0,(1±√5)/2}