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

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<cmath>x^2+y^2+z^2=\boxed{003}</cmath>
 
<cmath>x^2+y^2+z^2=\boxed{003}</cmath>
  
==See also==
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==See Also==
*[[Mock AIME 2 2006-2007/Problem 10 | Previous Problem]]
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http://www.artofproblemsolving.com/Wiki/index.php/1973_USAMO_Problems/Problem_4
*[[Mock AIME 2 2006-2007/Problem 12 | Next Problem]]
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{{Mock AIME box|year=2006-2007|n=2|num-b=10|num-a=12}}
*[[Mock AIME 2 2006-2007]]
 

Latest revision as of 20:55, 20 October 2019

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

http://www.artofproblemsolving.com/Wiki/index.php/1973_USAMO_Problems/Problem_4

Mock AIME 2 2006-2007 (Problems, Source)
Preceded by
Problem 10
Followed by
Problem 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15