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

Latest revision as of 20:55, 20 October 2019

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

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

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

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

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 ==Solution==
-The sums of the squares of the roots is given in the problem; 3.
+The roots are <math>x</math>, <math>y</math>, and <math>z</math>, and we add the squares:
+<cmath>x^2+y^2+z^2=\boxed{003}</cmath>
+==See Also==
-----
+http://www.artofproblemsolving.com/Wiki/index.php/1973_USAMO_Problems/Problem_4
+{{Mock AIME box|year=2006-2007|n=2|num-b=10|num-a=12}}
-*[[Mock AIME 2 2006-2007/Problem 10 | Previous Problem]]
-*[[Mock AIME 2 2006-2007/Problem 12 | Next Problem]]
-*[[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.