Question

高一 集合数学题

已知集合p的元素为1,m,m的二次方-3m-3,若3属于(符号)p,且-1不属于(符号)p,求实数m的值

Answer 1

P={1,m,m^2-3m-3}
3属于P
then
case 1
m=3

case 2
m^2-3m-3 = 3
m^2-3m-6 =0
m = (3 +√33)/2 or (3 -√33)/2

case 1 or case 2
m=3 or (3 +√33)/2 or (3 -√33)/2 --(1)

-1不属于P
then m is not equal to -1
and
if m^2-3m-3 = -1
m^2-3m-4 = 0
(m-4)(m+1)= 0
m = -1 or 4
∴ m is not equal to -1 or 4 --(2)

(1) and (2), we get
m=3 or (3 +√33)/2 or (3 -√33)/2 #