Difference between revisions of "1990 AIME Problems/Problem 15"

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== Problem ==
 
== Problem ==
 
Find <math>a_{}^{}x^5 + b_{}y^5</math> if the real numbers <math>a_{}^{}</math>, <math>b_{}^{}</math>, <math>x_{}^{}</math>, and <math>y_{}^{}</math> satisfy the equations
 
Find <math>a_{}^{}x^5 + b_{}y^5</math> if the real numbers <math>a_{}^{}</math>, <math>b_{}^{}</math>, <math>x_{}^{}</math>, and <math>y_{}^{}</math> satisfy the equations
<center><math>ax + by = 3^{}_{},</math></center>
+
<cmath>ax + by = 3^{}_{},</cmath>
<center><math>ax^2 + by^2 = 7^{}_{},</math></center>
+
<cmath>ax^2 + by^2 = 7^{}_{},</cmath>
<center><math>ax^3 + by^3 = 16^{}_{},</math></center>
+
<cmath>ax^3 + by^3 = 16^{}_{},</cmath>
<center><math>ax^4 + by^4 = 42^{}_{}.</math></center>
+
<cmath>ax^4 + by^4 = 42^{}_{}.</cmath>
  
 
== Solution ==
 
== Solution ==

Revision as of 18:28, 15 October 2007

Problem

Find $a_{}^{}x^5 + b_{}y^5$ if the real numbers $a_{}^{}$, $b_{}^{}$, $x_{}^{}$, and $y_{}^{}$ satisfy the equations \[ax + by = 3^{}_{},\] \[ax^2 + by^2 = 7^{}_{},\] \[ax^3 + by^3 = 16^{}_{},\] \[ax^4 + by^4 = 42^{}_{}.\]

Solution

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See also

1990 AIME (ProblemsAnswer KeyResources)
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Problem 14
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