Question 1123954: While doing his homework, Bryan thought about the football game, which is why he made a mistake. Instead of raising a number to the second power, he doubled it and got a two-digit number; this was the reverse of the correct answer. What was the correct answer?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
In Math, I know "an opposite number" - it is " -x ", the number with the opposite sign.
I also know "an inverse number" - it is  .
But I don't know what "the reverse number" means.
If it is the number with reversed digits, then the solution is as follows.
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.
Answer. x = 9.
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