2000 AMC 12 Problems/Problem 20
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Problem
If 
and 
are positive numbers satisfying
Then what is the value of 
?
Contents |
Solution
Solution 1
Multiplying all three expressions together,
Thus 
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 
.
See also
| 2000 AMC 12 (Problems • 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 | ||
