2013 AMC 12B Problems/Problem 6
- The following problem is from both the 2013 AMC 12B #6 and 2013 AMC 10B #11, so both problems redirect to this page.
Problem
Real numbers and satisfy the equation . What is ?
If we move every term dependent on or to the LHS, we get . Adding to both sides, we have . Notice this is a circle with radius , which only contains one point. We can split the into and to get . So, the only point is , so the sum is