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 | ||
− | < | + | <cmath>ax + by = 3^{}_{},</cmath> |
− | < | + | <cmath>ax^2 + by^2 = 7^{}_{},</cmath> |
− | < | + | <cmath>ax^3 + by^3 = 16^{}_{},</cmath> |
− | < | + | <cmath>ax^4 + by^4 = 42^{}_{}.</cmath> |
== Solution == | == Solution == |
Revision as of 18:28, 15 October 2007
Problem
Find if the real numbers , , , and satisfy the equations
Solution
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See also
1990 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Last question | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |