2006 Alabama ARML TST Problems/Problem 13
Problem
Find the sum of the solutions to the equation
Solution
There are four solutions, since we have fourth roots. We try to find some nice solutions:
Not quite, but
That's a solution! Now we switch:
Another solution. But we see that . So we try to prove that if is a solution, then is a solution:
We plug in for y and we get
But that just equals four! Thus, if is a solution, then is a solution.
Since there are four roots,