DSE 2009 Simple Maximization Question

[ElPsyCongroo]

Isn't x=1 y=0 a unique solution for this?

Answer is no solution as per Amit sir's key http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/dse2009_ans.pdf

[vishp]

Using Lagrangin optimization method,
L=x^2-y^2+p(1-x-y)
dL/dx=2x-p=0....(1)
dL/dy=-2y-p=0.... (2)
dL/dp=1-x-y=0....(3)
(1)/(2) gives, -x=y. put this value in (3), you will get 1=0.. this is not possible at all.. so answer is no solution.

[ElPsyCongroo]

https://www.desmos.com/calculator/ax6ktngcae

I completely overlooked the fact that x and y belong to real numbers, not just positive real numbers, woops. I see now.