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> | + | <math>x+y+z=3,~x^2+y^2+z^2=3,~x^3+y^3+z^3 =3.</math> |
| − | == | + | ==Solution== |
| − | + | 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}} | ||
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
Solution
The roots are 
, 
, and 
, and we add the squares:
![\[x^2+y^2+z^2=\boxed{003}\]](http://latex.artofproblemsolving.com/3/d/a/3da4045aa2f27c71d36e065dcea56e174350573a.png)
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 | ||
