Difference between revisions of "2006 SMT/Algebra Problems/Problem 6"
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Revision as of 09:31, 28 May 2012
Problem
Let be real numbers satisfying:
Determine all possible values of .
Solution
From the first equation, we have . Plugging this into the third equation, we get . Multiplying both sides by , we get .
Now we plug that into the second equation. We have . Getting rid of the fractions, we have . We can factor that as , so or .
If , then and , so .
If , then and , so .
Therefore, the possible values of are .