试题与答案

已知条件p:4xx-3<1,条件q:5x-6>x2,则p是q的( ) A.必要不充

题型:选择题

题目:

已知条件p:
4x
x-3
<1
,条件q:5x-6>x2,则p是q的(  )
A.必要不充分条件B.充分不必要条件
C.充要条件D.既不充分也不必要条件

答案:

条件p:

4x
x-3
<1即为
3x+3
x-3
<0
即为-1<x<3;

条件q:5x-6>x2即为x2-5x+6<0即为2<x<3;

因为{x|2<x<3}⊊{x|-1<x<3};

所以p成立q不一定成立,反之q成立p一定成立,

所以p是q的必要不充分条件,

故选A.

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