Need help to continue with the following solution: Find the stationary points of the function,
subject to the constraint,
Substituting for x in 
I've played with this system for a while and can't see any way to make it less of a nightmare. Whether or not you get the equation in x or in y you wind up with a quartic equation which just doesn't look like it's got nice solutions. You'll have to do it numerically. Looking at the graph of the x equation it looks like you've got 2 real solutions lurking. One is near x = 1/2 and the other is large and negative.