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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