Difference between revisions of "2024 AMC 8 Problems/Problem 22"
Rainier2020 (talk | contribs) (→Problem) |
Rainier2020 (talk | contribs) (→Solution) |
||
| Line 3: | Line 3: | ||
==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 13:18, 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 
