Hey guys, new here and this is my first post. Wondering if anyone could help me. 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.