Difference between revisions of "2016 AIME II Problems/Problem 3"
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Revision as of 20:15, 18 August 2020
Problem
Let and
be real numbers satisfying the system
,
,
,
Find the value of
.
Solution
First, we get rid of logs by taking powers: ,
, and
. Adding all the equations up and using the
property, we have
, so we have
. Solving for
by substituting
for
in each equation, we get
, so adding all the absolute values we have
.
Solution by Shaddoll
See also
2016 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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.