Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 11"

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==See also==
 
==See also==
*[[Mock AIME 2 2006-2007/Problem 10 | Previous Problem]]
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*[[Mock AIME 2 2006-2007 Problems/Problem 10 | Previous Problem]]
*[[Mock AIME 2 2006-2007/Problem 12 | Next Problem]]
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*[[Mock AIME 2 2006-2007 Problems/Problem 12 | Next Problem]]
 
*[[Mock AIME 2 2006-2007]]
 
*[[Mock AIME 2 2006-2007]]

Revision as of 15:33, 3 April 2012

Problem

Find the sum of the squares of the roots, real or complex, of the system of simultaneous equations

$x+y+z=3,~x^2+y^2+z^2=3,~x^3+y^3+z^3 =3.$

Solution

The roots are $x$, $y$, and $z$, and we add the squares:

\[x^2+y^2+z^2=\boxed{003}\]

See also