A two digit, positive integer,b, is formed by reversing the digits of another two digit, positive integer, a. If both a+b and a-b are perfect squares, what is the value of a?

NoobGuest Jun 16, 2019

#1**+3 **

Let a = 10n + m and b = 10m + n

Then a - b = 9(n - m)

and a + b = 11(n + m)

These are perfect squares if n - m = 1 and n + m = 11

i.e. n = 6 and m = 5

This makes a = 65 and b = 56

Alan Jun 16, 2019

#2**-1 **

Found It! file:///C:/Users/Jimin%20Bang/Desktop/Hard%20Problem%20Math%201.PNG

copy and paste it into a new tab.

NoobGuest Jun 16, 2019