Difference between revisions of "2005 AIME I Problems/Problem 6"
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Revision as of 12:22, 17 January 2007
Problem
Let be the product of the nonreal roots of Find
Solution
The left-hand side of that equation is nearly equal to . Thus, we add 1 to each side in order to complete the fourth power and get .
Let be the positive real fourth root of 2006. Then the roots of the above equation are for . The two non-real members of this set are and . Their product is . so .