Find the maxima and the minima of the given function given the constraint.
Using the Lagrange Multiplier method, I managed to obtain
Solving for the variables gave me:
So then I plug these values into my constraint to end up with
Then I end up with the quadratic, after simplifying;
However, this quadratic can't be solved using real numbers. Have I done anything wrong or am I using the wrong approach?
Because a specific value is NOT a part of the solution, I find it simplest to eliminate first. Here, instead of solving for x and y in terms of , I would use and to say that so that . Put that into the condition x+ y= 1 to get which is equivalent to . The discriminant for that quadratic equation is so, yes, there is no real value of x satisfying this problem.