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- Feb 14, 2012

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I've come across this problem recently:

If a²+b²=2 and (c-3)²+(d-4)²=1, find the maximum value of ad-bc.

I haven't solved it and actually, I don't know of any algebraic method I could use to solve it and I am wondering if this problem is doable with the Lagrange Multiplier method. However, as some of you know, I am new to this method, and I don't know how to handle multiple constraints.

If you're interested in this problem and want to share with me your idea on how to crack it using a purely algebraic method that would be fine, but if you could help me solve it using Lagrange Multipliers, I would like that too.

Thanks!