Difference between revisions of "2023 AIME I Problems/Problem 2"
m |
MRENTHUSIASM (talk | contribs) m (→Video Solution 1 by TheBeautyofMath) |
||
Line 17: | Line 17: | ||
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ||
− | ==Video Solution | + | ==Video Solution by TheBeautyofMath== |
https://youtu.be/U96XHH23zhA | https://youtu.be/U96XHH23zhA | ||
Revision as of 14:13, 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 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.