is directly proportional to the sum of the squares of and and inversely proportional to and the square of . If when and , find when and . (Thanks to Bicameral of the AoPS forum for this one)
First, let's write these out algebraically: the first is , the second is , and the third is . Plugging the values into the first equation gives , so . The second gives , and the third gives . We can use any of these three to solve the problem. Using the second gives us , so the answer is .