How do I find the point of intersection of $ + - + 2 = 0$ and $^2 = ^2 + ^2$ that is closest to the origin?
I know I have to use the LaGrange multiplier in order to minimize the equation $$ (,,) = ^2 + ^2 + ^2. $$ So I have the following:
- $2 = λ + μ(2)$
- $2 = λ + μ(2)$
- $2 = -λ + μ(-2)$
- $ + - + 2 = 0$
- $^2 = ^2 + ^2$
But I keep getting that $ = 0$ which has no solution.