- #1

KaGa

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So I've encountered a problem on Lagrange's undetermined multiplier. Usually i have no problem with these, but this one caught me off a little.

g(x,y) = x^2 + y^2 - 4xy - 6 = 0

Find the points closest to the origin.

With this in mind:

f(x,y) = x^2 + y^2

Using the formula:

d(f + λg) = 0

Let (f + g) = F

F_x = 2x + 2λx -λ4y

F_y = 2y + 2λy -λ4x

By inspection you can see x = y, so into g(x,y) and...

-2x^2-6=0

x^2 = -3

∴ x = √-3

I haven't encountered an imaginary point yet in this type of question, and since i can't quite make sense of it in my mind, i was wondering if anyone could help me? Have I made an error somewhere, or can you have imaginary points closest to the origin?

Cheers.