Question 703403
Let the two integers be x and y.

x^2 + y^2 = 97

x + y = 13 => x = 13 - y

(13 - y)^2 + y^2 = 97

169 - 26y + 2y^2 = 97

2y^2 - 26y + 72 = 0

y^2 - 13y + 36 = 0

(y - 9)(y - 4) = 0 => y = 4, 9

x = 9, 4