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 01:48, 2 March 2007
Problem
Find if the real numbers
,
,
, and
satisfy the equations
![$ax + by = 3^{}_{},$](http://latex.artofproblemsolving.com/f/8/1/f818f014e367cbc484a1e6e85145050360315398.png)
![$ax^2 + by^2 = 7^{}_{},$](http://latex.artofproblemsolving.com/3/7/5/375cb1ff615d05f5f539db155a695e995ac36c03.png)
![$ax^3 + by^3 = 16^{}_{},$](http://latex.artofproblemsolving.com/2/8/4/284e7ba5ef0391d5a7bdc3c7b499ba22b190680a.png)
![$ax^4 + by^4 = 42^{}_{}.$](http://latex.artofproblemsolving.com/b/a/7/ba7475fbcb37c22bc122859ba939330f2d45a8dd.png)
Solution
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