Find the minimum and maximum values of $f(x, y) = x^2− xy + y^2$ inside the quarter circle given by $x^2+ y^2\le 1$, constraint $x, y\ge0$.
I set out the equations $$ 2x-y=2 \lambda x + 2 \lambda y, \quad 2y-x = 2 \lambda x + 2 \lambda y \quad \text{and} \quad x^2+y^2\le1.$$
However I cannot cancel out the variables to find $\lambda$. How am I meant to approach this question?
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https://mast.queensu.ca/~math121/Assignments/Unit23_solutions.pdf