- #1
rocomath
- 1,755
- 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: