2024 AMC 8 Problems/Problem 22
Problem 22
Solution
Factoring yields . Denote to be solutions of this polynomial. We can easily find one of the solutions is . Using the quadratic formula on the rest of the factors yields and finally . The sum is 1, so 1 to the third power is 1. So, the final answer is .
Sidenote: You also could have used Newtonian sums to solve this problem.