Difference between revisions of "2024 AMC 8 Problems/Problem 22"
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==Solution== | ==Solution== | ||
| − | + | Factoring <math>x^5+2x^4+3x^3+3x^2+2x+1</math> yields <math>(x+1)(x^2+1)(x^2+x+1)</math>. We can easily find one of the solutions is <math>x=-1</math>. Using the quadratic formula on the rest of the factors yields <math>-i, i, \frac{-1-i sqrt(3)}{2}</math> | |
Revision as of 14:18, 21 January 2024
Problem 22
What is the sum of the cubes of the solutions cubed of 
?
Solution
Factoring 
yields 
. We can easily find one of the solutions is 
. Using the quadratic formula on the rest of the factors yields 
