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NewtonianAlch
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Homework Statement
Find the points [itex]x^2 + xy + y^2 = 2[/itex] that are closest to the origin.
Homework Equations
Distance Formula
The Attempt at a Solution
I have to first solve this without using Lagrange Multipliers.
This is essentially an ellipse. So I first completed the square:
[itex]3/4\,{x}^{2}+ \left( y+1/2\,x \right) ^{2}=2[/itex]
I was thinking first I should separate [itex]x[/itex] and [itex]y[/itex], and use that in the distance formula, but I can't seem to isolate [itex]y[/itex], is my approach wrong?
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