1. The problem statement, all variables and given/known data Find the extrema of the given function subject to the given constraint: f(x,y)=x2-2xy+2y2, subject to x2+y2=1 2. Relevant equations Lagrange Multipliers 3. The attempt at a solution First, I defined the constraint to be g(x,y)=0, that is, g(x,y)=x2+y2-1 I then set up the usual basic system of equations (I did not show my work for this part because I find it unnecessary): x-y=[tex]\lambda[/tex]x -x+2y=[tex]\lambda[/tex]y x2+y2-1=0 (*Note: I reduced the first two equations by a factor of 2 for the sake of easier computing). So now, I have three sets of equation and the MOST algebraic manipulation I could do is the following: y=x(1-[tex]\lambda[/tex]) x=y(2-[tex]\lambda[/tex]) x^2+y^2=1 _________________________________________ Another path I took was combining the first two equations, which got me: [tex]\lambda[/tex](x+y)=y Which got me no where. _________________________________________ And now, I am stuck! Oh yes, I forgot to mention that I am not allowed to use polar coordinates at all (since the constraint is a unit circle...) - I am only allowed to use Lagrange Multipliers. On another note, the answer is very, very ugly (it is in decimals). Can anyone please show me how to figure this problem out? Thanks!