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, the answer is
See also
2006 Alabama ARML TST (Problems) | ||
Preceded by: Problem 12 |
Followed by: Problem 14 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |