2024 AMC 8 Problems/Problem 22
Problem 22
What is the sum of the cubes of the solutions cubed of ?
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 3, so 3 to the third power is \boxed{27}.