Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 4"
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<math>\zeta_1, \zeta_2,</math> and <math>\zeta_3</math> are complex numbers such that | <math>\zeta_1, \zeta_2,</math> and <math>\zeta_3</math> are complex numbers such that | ||
| − | <math>\zeta_1 + \zeta_2 + \zeta_3 = 1 | + | <math>\begin{align*}\zeta_1+\zeta_2+\zeta_3&=1\\ |
| − | + | \zeta_1^2+\zeta_2^2+\zeta_3^2&=3\\ | |
| − | + | \zeta_1^3+\zeta_2^3+\zeta_3^3&=7\end{align*}</math> | |
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==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
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Revision as of 01:31, 23 April 2008
Problem
and 
are complex numbers such that
$\begin{align*}\zeta_1+\zeta_2+\zeta_3&=1\\ \zeta_1^2+\zeta_2^2+\zeta_3^2&=3\\ \zeta_1^3+\zeta_2^3+\zeta_3^3&=7\end{align*}$ (Error compiling LaTeX. Unknown error_msg)
Compute 
.
Solution
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