2001 AMC 10 Problems/Problem 10
Contents
[hide]Problem
If , , and are positive with , , and , then is
Solution 1
Look at the first two equations in the problem.
and .
We can say that .
Given , we can substitute for and find
.
We can replace y into the first equation. .
Since we know every variable's value, we can substitute it in for .
Solution 2
These equations are symmetric, and furthermore, they use multiplication. This makes us think to multiply them all. This gives . We square root: . Aha! We divide each of the given equations into this, yielding , , and . The desired sum is , so the answer is .
See Also
2001 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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All AMC 10 Problems and Solutions |