# Minimizing $$l(x,y)$$

Calculus Level 4

If the minimum value of the $$l(x,y)$$ is of the form $$\dfrac{A}{B}$$, where $$A$$ and $$B$$ are co-prime integers, then find the value of $$A+B$$.

$l(x,y)=(x-y)^2+(x^2-3y+5)^2 \ \ \ \forall \ x,y \in \mathbb{R}$

$$\textbf {Note :}$$ You may not use wolfram alpha or similar software.

$$\textbf{Extra credit :}$$ Post a solution without evaluating partial derivatives

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