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 |