SOLUTION: Find the 2 digit number which has the square of the sum of its digits equal to the number obtained by reversing it digit?

Question 760846: Find the 2 digit number which has the square of the sum of its digits equal to the number obtained by reversing it digit?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
10a+b = a two digit number
:
write what it says:
:
"A 2 digit number which has the square of the sum of its digits
equal to the number obtained by reversing it's digit?"
(a+b)^2 = 10b + a
We have two unknown with only one equation
Assume a = 1, find b
(1+b)^2 = 10b + 1
1 + 2b + b^2 = 10b + 1
:
b^2 + 2b - 10b = 1 - 1
b^2 - 8b = 0
divide both sides by b
b - 8= 0
b = 8
then the number is 18; (9^2 = 81)
:
I don't think there is any other number, except perhaps 10
(1+0)^2 = 0 + 1

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