- #1

- 1,752

- 1

(1) [tex]f(x,y,z)=x+2y[/tex]

(2) [tex]x+y+z=1[/tex]

(3) [tex]y^2+z^2=4[/tex]

[tex]1=\lambda[/tex]

[tex]2=\lambda+2y\mu[/tex]

[tex]0=\lambda+2z\mu[/tex]

[tex]u=\frac{1}{2y}[/tex]

[tex]y=\pm\sqrt2 \ \ \ z=\pm\sqrt2[/tex]

Plugging into equation 2 to solve for x.

How do I know to use either [tex]y=\sqrt 2 \ \mbox{or} \ y=-\sqrt2[/tex] ... similarly with my values for z.

edit: NVM, I'm an idiot :p I overlooked a step, which told me that [tex]z=-y[/tex]

... too late to delete?

(2) [tex]x+y+z=1[/tex]

(3) [tex]y^2+z^2=4[/tex]

[tex]1=\lambda[/tex]

[tex]2=\lambda+2y\mu[/tex]

[tex]0=\lambda+2z\mu[/tex]

[tex]u=\frac{1}{2y}[/tex]

[tex]y=\pm\sqrt2 \ \ \ z=\pm\sqrt2[/tex]

Plugging into equation 2 to solve for x.

How do I know to use either [tex]y=\sqrt 2 \ \mbox{or} \ y=-\sqrt2[/tex] ... similarly with my values for z.

edit: NVM, I'm an idiot :p I overlooked a step, which told me that [tex]z=-y[/tex]

... too late to delete?

Last edited: