Art of Problem Solving

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

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*[[Mock AIME 2 2006-2007]]
*[[Mock AIME 2 2006-2007]]
== Problem Source==
This problem was given to 4everwise by a friend, Henry Tung. Upper classmen bullying freshmen. (Just kidding; it's a nice problem. [[Image:Razz.gif]]) This problem is also incredibly similar to 1973 USAMO problem 4.

Revision as of 13:57, 16 December 2007

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 sums of the squares of the roots is given in the problem; 3.