2000 AMC 12 Problems/Problem 20
Problem
If and are positive numbers satisfying
Then what is the value of ?
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 |
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