2022 AIME II Problems/Problem 4
Problem
There is a positive real number not equal to either
or
such that
The value
can be written as
, where
and
are relatively prime positive integers. Find
.
Solution
We could assume a variable which equals to both
and
.
So that (Eq1)
and
(Eq2)
Express Eq1 as: (Eq3)
Substitute Eq2 to Eq3:
Thus, , where
and
.
Therefore, .
~DSAERF-CALMIT
See Also
2022 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
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