2000 AMC 12 Problems/Problem 20
Problem
If and
are positive numbers satisfying
Then what is the value of ?
Contents
[hide]Solution
Solution 1
We multiply all given expressions to get:
Adding all the given expressions gives that
We subtract
from
to get that
. Hence, by inspection,
.
~AopsUser101
Solution 2
We have a system of three equations and three variables, so we can apply repeated substitution.
Multiplying out the denominator and simplification yields , so
. Substituting leads to
, and the product of these three variables is
.
Also see
2000 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 19 |
Followed by Problem 21 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.