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

Revision as of 00:48, 2 March 2007

Find $a_{}^{}x^5 + b_{}y^5$ if the real numbers $a_{}^{}$ , $b_{}^{}$ , $x_{}^{}$ , and $y_{}^{}$ satisfy the equations

$ax + by = 3^{}_{},$ $ax^2 + by^2 = 7^{}_{},$ $ax^3 + by^3 = 16^{}_{},$ $ax^4 + by^4 = 42^{}_{}.$

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-{{empty}}
 == 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
+<center><math>ax + by = 3^{}_{},</math></center>
+<center><math>ax^2 + by^2 = 7^{}_{},</math></center>
+<center><math>ax^3 + by^3 = 16^{}_{},</math></center>
+<center><math>ax^4 + by^4 = 42^{}_{}.</math></center>
 == Solution ==