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.
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.