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Homework Statement
Find the optima of [itex]f(x, y)[/itex] which satisfy the equation [itex]g(x, y) = 3[/itex] and [itex]x > 0[/itex].
Homework Equations
[itex]f(x, y) = x + y[/itex]
[itex]g(x, y) = x^2 + xy + y^2[/itex]
[itex]\nabla f(x, y) = (1, 1)[/itex]
[itex]\nabla g(x, y) = (2x + y, 2y + x)[/itex]
The Attempt at a Solution
[itex]\nabla f(x, y) = \lambda \nabla g(x, y) <=> x = y => f(x, x) = f(x) = 2x => g(x, x) = g(x) = 3x^2 = 3 <=> x = y = 1 (x > 0) => f(1, 1) = 2[/itex].
Now, how do I get the minima...?
Minima is supposed to be [itex]-\sqrt{3}[/itex].