Question

命题p:实数x满足x^2-4ax+3a^2<0(其中a>0)

命题p:实数x满足x^2-4ax+3a^2<0(其中a>0)，命题q:实数x满足{|x-1|<=2;x+3/x-2>=0.(1)若a=1,且p^q为真，求实数x的取值范围;(2)若非p是非q的充分不必要条件，求实数a的取值范围

Answer 1

命题p:实数x满足x^2-4ax+3a^2<0(其中a>0)，
即a<x<3a,
命题q:实数x满足{|x-1|<=2;(x+3)/(x-2)>=0},
即-1<=x<=3,且“x<=-3或x>2”，
亦即2<x<=3.
(1)p:1<x<3,
p∧q为真，x的取值范围是2<x<3.
(2)非p是非q的充分不必要条件,
<==>q是p的充分不必要条件,
<==>{a<=2,3<3a},
<==>1<a<=2.