The sum of the squares of two consecutive positive integers is 61. Find these two numbers.

The sum of the squares of two consecutive positive integers is 61. Find these two numbers.

Let the 2 consecutive integers be x and x + 1. We have:
x^2 + (x + 1)^2 = 61

Simplify:
x^2 + x^2 + 2x + 1 = 61
2x^2 + 2x + 1 = 61

Subtract 61 from each side:
2x^2 + 2x - 60 = 0

Divide each side by 2
x^2 + x - 30

Using our quadratic equation calculator, we get:
x = 5 and x = -6

The question asks for positive integers, so we use x = 5. This means the other number is 6.