the product of four distinct positive integers x, y, z, a is 8. The number also satisfy xy + x + y + 1 = 323 and yz + y + z+ 1 = 399. then find the value of a.
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the product of four distinct positive integers can not be 8.
Here is why:
As they are distinct positive integers, and their product is 8, none of them can be more than 8.
Now, if one of them is 8, then the rest three have to be 1, hence they fail to be distinct.
If one of them is 7, then its product with other integers can not make 8, so this case is impossible.
If one of them is 6, then its product with other integers can not make 8, so this case is impossible.
If one of them is 5, then its product with other integers can not make 8, so this case is impossible.
If one of them is 4, then the product of the other three has to be 8/4=2, then two of them must be 1 and one is 2, which is not possible as they have to be distinct.
If one of them is 3, then its product with other integers can not make 8, so this case is impossible.
If one is 2, then the product of the other three has to be 8/2=4, then the three numbers are either 2,2,1 or 4,1,1, which is not possible as they have to be distinct.
If one of them is 1, then the product of the other three has to be 8/1=8, then the three numbers are either 8,1,1 or 4,2,1 or 2,2,2 which is not possible as they have to be distinct.
Recheck your question or please be a little specific about the name of the chapter/textbook to which you are referring here so that we can provide you with some meaningful help. Look forward to hearing from you again! Regards
the product of four distinct positive integers can not be 8.
Here is why:
As they are distinct positive integers, and their product is 8, none of them can be more than 8.
Now, if one of them is 8, then the rest three have to be 1, hence they fail to be distinct.
If one of them is 7, then its product with other integers can not make 8, so this case is impossible.
If one of them is 6, then its product with other integers can not make 8, so this case is impossible.
If one of them is 5, then its product with other integers can not make 8, so this case is impossible.
If one of them is 4, then the product of the other three has to be 8/4=2, then two of them must be 1 and one is 2, which is not possible as they have to be distinct.
If one of them is 3, then its product with other integers can not make 8, so this case is impossible.
If one is 2, then the product of the other three has to be 8/2=4, then the three numbers are either 2,2,1 or 4,1,1, which is not possible as they have to be distinct.
If one of them is 1, then the product of the other three has to be 8/1=8, then the three numbers are either 8,1,1 or 4,2,1 or 2,2,2 which is not possible as they have to be distinct.
Recheck your question or please be a little specific about the name of the chapter/textbook to which you are referring here so that we can provide you with some meaningful help. Look forward to hearing from you again! Regards