Difference between revisions of "2023 AIME I Problems/Problem 2"
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~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ||
+ | ==Video Solution 1 by TheBeautyofMath== | ||
+ | https://youtu.be/U96XHH23zhA | ||
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+ | ~IceMatrix | ||
==See also== | ==See also== | ||
{{AIME box|year=2023|num-b=1|num-a=3|n=I}} | {{AIME box|year=2023|num-b=1|num-a=3|n=I}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 06:56, 13 February 2023
Problem
Positive real numbers and satisfy the equations The value of is where and are relatively prime positive integers. Find
Solution
Denote . Hence, the system of equations given in the problem can be rewritten as Solving the system gives and . Therefore, Therefore, the answer is .
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
Video Solution 1 by TheBeautyofMath
~IceMatrix
See also
2023 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.