AoPS Wiki talk:Problem of the Day/August 2, 2011
Revision as of 04:04, 2 August 2011 by BoyosircuWem (talk | contribs)
Problem: Find all such that and .
Solution: Let and . Then and . Hence, This quartic has two real roots; and by the cubic formula. Call this second root (which evaluates to about -3.01) . The two real solutions are therefore: and
There are more solutions in , corresponding to the complex roots of .