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

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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 == Problem ==
-The positive integers <math>\displaystyle x_1, x_2, ... , x_7</math> satisfy <math>\displaystyle x_6 = 144</math> and <math>\displaystyle x_{n+3} = x_{n+2}(x_{n+1}+x_n)</math> for <math>\displaystyle n = 1, 2, 3, 4</math>. Find <math>\displaystyle \lfloor x_7 /10 \rfloor </math>.
+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>
+==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}}