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

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Find the sum of the squares of the roots, real or complex, of the system of simultaneous equations
 
Find the sum of the squares of the roots, real or complex, of the system of simultaneous equations
  
<math>x+y+z=3, x^2+y^2+z^2=3,x^3+y^3+z^3 =3.</math>
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<math>x+y+z=3,~x^2+y^2+z^2=3,~x^3+y^3+z^3 =3.</math>
  
== Problem Source==
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==Solution==
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]])
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The roots are <math>x</math>, <math>y</math>, and <math>z</math>, and we add the squares:
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<cmath>x^2+y^2+z^2=\boxed{003}</cmath>
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==See Also==
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http://www.artofproblemsolving.com/Wiki/index.php/1973_USAMO_Problems/Problem_4
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{{Mock AIME box|year=2006-2007|n=2|num-b=10|num-a=12}}

Latest revision as of 21:55, 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
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