The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?

9, 10

11, 12

12, 13

10, 11

Let the two consecutive positive integers be x and x + 1

x2 + (x + 1)2 - x(x + 1) = 91

x2 + x - 90 = 0

(x + 10)(x - 9) = 0 => x = -10 or 9.

As x is positive x = 9

Hence the two consecutive positive integers are 9 and 10.