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 | ||
+ | <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 == | == Solution == |
Revision as of 00:48, 2 March 2007
Problem
Find if the real numbers , , , and satisfy the equations
Solution
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