2020 AIME II Problems/Problem 3
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Contents
Problem
The value of that satisfies
can be written as
, where
and
are relatively prime positive integers. Find
.
Solution
Let . Based on the equation, we get
and
. Expanding the second equation, we get
. Substituting the first equation in, we get
, so
. Taking the 100th root, we get
. Therefore,
, so
and the answer is
.
~rayfish
Video Solution
https://www.youtube.com/watch?v=lPr4fYEoXi0 ~ CNCM