Answer: 7 and 8
Explanation:
Let x represent the first number, then x + 1 is the other number.
(x)² + (x + 1)² = 113
x² + x² + 2x + 1 = 113 expanded (x + 1)²
2x² + 2x + 1 = 113 added like terms
2x² + 2x - 112 = 0 subtracted 113 from both sides
x² + x - 56 = 0 divided both sides by 2
(x + 8) (x - 7) = 0 factored polynomial
x + 8 = 0 x - 7 = 0 applied zero product property
x = -8 x = 7 solved for x
↓
not valid since the restriction is that x > 0 (a positive number)
So, x = 7 and x + 1 = (7) + 1 = 8