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问题 填空题

关于x的方程x2+a|x|+a2-9=0（a∈R）有唯一的实数根，则a=______．

答案

令f（x）=x2+a|x|+a2-9

则f（-x）=f（x）=x2+a|x|+a2-9恒成立

故函数f（x）为偶函数，其图象关于Y轴对称，

若关于x的方程x2+a|x|+a2-9=0（a∈R）有唯一的实数根，

则函数f（x）有且只有一个零点，

则f（0）=0，解得a=±3

又当a=-3时，函数f（x）有3个零点，

∴a=3

故答案为：3

单项选择题

When is the t- distribution the appropriate distribution to use The t -distribution is the appropriate distribution to use when constructing confidence intervals based on:（）

A. small samples from populations with known variance that are at least approximately normal.

B. large samples from populations with known variance that are nonnormal.

C. small samples from populations with unknown variance that are at least approximately normal.
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