Bunuel wrote:
Official Solution:
If \((|p|!)^p = |p|!\), which of the following could be true?
I. \(p=-1\)
II. \(p=0\)
III. \(p=1\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
Important properties: \(0!=1\) and any non-zero number to the power of 0 is 1.
Let's check the options:
If \(p=-1\) then \((|p|!)^p = (|-1|!)^{-1}=1^{-1}=1\) and \(|p|!=|-1|!=1!=1\) so \(p\) could be -1;
If \(p=0\) then \((|p|!)^p = (|0|!)^{0}=1^{0}=1\) and \(|0|!=0!=1\) so \(p\) could be 0;
If \(p=1\) then \((|p|!)^p = (|1|!)^{1}=1^{1}=1\) and \(|p|!=|1|!=1\) so \(p\) could be 1.
Answer: E
Hi
In one of your article you mentioned that factorial of negative numbers is undefined so how here you are considering-1!=1?
>> !!!
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