2023 AIME I Problems/Problem 2
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 our system gives
and
.
Therefore,
Therefore, the answer is
.
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
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 |
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