Explanation:

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.