题目内容
如图,正四棱柱
中,设
,
,
若棱
上存在点
满足
平面
,求实数
的取值范围



若棱






如图,以点
为原点
,
分别为
轴建立
空间直角坐标系
,则
,
,
,
设
,其中
, …………………………3分
因为
平面
,
所以
,
即
, …………………………6分
化简得
,
, …………………………8分
故判别式
,且
,
解得
2.





空间直角坐标系




设


因为



所以

即

化简得


故判别式



解得


略

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