06/19/2020 (2011: Countdown Round, Problem 13)

Q: The sum of the squares of the two numbers is 36 more than twice the product of the two numbers. What is the positive difference between the two numbers?

A: 6

Let's say the numbers are a and b, then:

a² + b² = 36 + 2(ab)

If we put variables on one side, then we get:

a² - 2ab + b² = 36

We factor it and get:

(a - b)² = 36

We find the square root of both sides:

a - b = 6

That means the positive difference between the two numbers is 6.