Question 1123954
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        In Math, I know "an opposite number" - it is " -x ", the number with the opposite sign.


        I also know "an inverse number" - it is    {{{1/x}}}.


        But I don't know what "the reverse number" means.



If it is the number with reversed digits, then the solution is as follows.



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Let  x is the original number, which is  under the question.


It is clear that under given condition, x is one-digit number.


Then  2x = 10a + b,  the two-digit number with the "tens" digit "a" and the "ones" digit "b".


The condition says


    2x = 10a + b,  while  x^2 = 10b + a.


       T A B L E 

  x   2x= 10a+b      x^2= 10b+a
----------------------------- -------

  1      2
  2      4
  3      6
  4      8             16
  5     10             25
  6     12             36
  7     14             49
  8     16             64
  9     18             81


From the Table, you see that 

    (a)  2x is a two-digits number only for  5 <= x <= 9,   and

    (b)  in this case,  the "tens" digit of 2x is 1.

         It means that x^2 has the "ones" digit 1. 


The only square of an integer number between 5 and 9, which is ended by 1, is 9.


And this number, x= 9, satisfies all the conditions.


<U>Answer</U>.  x = 9.
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