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$x$ and $y$ are real numbers where satisfied the equation $x^2+y^2+xy-3x-3y-9=0$

Find the max. and min. values of $x^2+y^2$

I don't know how to find the constraint

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the constraint is you're confined to the subset of $\mathbb{R}^2$ cut out by $x^2 + y^2 + xy - 3x - 3y - 9 = 0$ –  uncookedfalcon Nov 20 '12 at 3:54
    
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Ok, next time i will do this –  cwk709394 Nov 20 '12 at 4:44
    
You should consider accepting the answers to some of your previous questions as well. –  Rahul Nov 20 '12 at 5:00
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1 Answer

up vote 1 down vote accepted

Your constraint is the curve $$x^2+y^2+xy-3x-3y-9=0$$ Hence, you need to consider the function $$f(x,y; \lambda) = x^2 + y^2 + \lambda (x^2+y^2+xy-3x-3y-9)$$ and differentiate with respect to $x,y$ and $\lambda$ and find the critical points.

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oh, thanks a lot –  cwk709394 Nov 20 '12 at 4:02
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