Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 4"
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\zeta_1^2+\zeta_2^2+\zeta_3^2&=3\\ | \zeta_1^2+\zeta_2^2+\zeta_3^2&=3\\ | ||
\zeta_1^3+\zeta_2^3+\zeta_3^3&=7\end{align*}</math> | \zeta_1^3+\zeta_2^3+\zeta_3^3&=7\end{align*}</math> | ||
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Compute <math>\zeta_1^{7} + \zeta_2^{7} + \zeta_3^{7}</math>. | Compute <math>\zeta_1^{7} + \zeta_2^{7} + \zeta_3^{7}</math>. | ||
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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