SOLUTION: The sum of a two digit number and the number obtained by reversing its digits is a square number. How many such numbers are there?
Algebra.Com
Question 1080520: The sum of a two digit number and the number obtained by reversing its digits is a square number. How many such numbers are there?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let be the first digit, and let be the second digit.
The value of the number is .
The value of the number obtained by reversing its digits is .
Their sum is
.
For that sum to be the square of an integer, it must be true that
.
There are possible pastors of digits adding to :
,
,
, and
.s
Since we can make two 2-digit number out of each paiR
by changing the other of the digits,
there are numbers that could be
the original 2-digit number in the problem.
RELATED QUESTIONS
Find all two-digit numbers that give a sum of 154 when the original number and the number (answered by stanbon)
the sum of a two digit number and obtained by reversing the order of its digit is 99.if... (answered by ibworldacademy)
a two-digit number is equal to 3 times the sum of its digits.if the number obtained by... (answered by stanbon)
the sum of two digit number and the number obtained by reversing the order of its digits... (answered by lwsshak3)
A two-digit number is eight times the sum of its digit. When the number is added to the... (answered by ankor@dixie-net.com)
The tens' digit of a certain two-digit number is twice the units' digit. The difference... (answered by ankor@dixie-net.com)
6 times the sum of the digits of a two digit number is 1 less than the number obtained by (answered by ankor@dixie-net.com)
The difference between the digits of a digit number is 4. The sum of the numbers and the... (answered by ankor@dixie-net.com)
A certain number is less than a number obtained by reversing the digits by 9.Also the sum (answered by Alan3354,ikleyn)