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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?

 Jun 16, 2019
 #1
avatar+28176 
+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

 Jun 16, 2019
 #3
avatar+208 
-1

Yes You are correct...

NoobGuest  Jun 16, 2019
 #2
avatar+208 
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Found It! file:///C:/Users/Jimin%20Bang/Desktop/Hard%20Problem%20Math%201.PNG  

copy and paste it into a new tab.

 Jun 16, 2019
edited by NoobGuest  Jun 16, 2019
 #4
avatar+208 
-1

That is what the website says

NoobGuest  Jun 16, 2019
 #5
avatar+208 
-1

I posted this question, just to see like another point of view from the Websites cuz the website sometimes confuses me...

NoobGuest  Jun 16, 2019

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