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Mock AIME 2 2006-2007 Problems/Problem 11

Revision as of 11:01, 10 February 2008 by 1=2 (talk | contribs) (→‎Solution)

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

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