If x2 - y2 = 23  What does  x2 + y2 =???

Solution Below

Using the concept of difference of 2 squares factor x2 - y2= 23 into (x+y)(x-y)=23. 

Since 23 is Prime its factors are 1 and 23.

Thus x+y = 23 and x-y = 1

Adding the 2 equations gives 2x = 24 Thus x=12, and y=11

x2 + y2 = 122 + 112 = 144 + 121 = 265

Answer x2 + y2 = 265