Question

Use lagrange multiplier to find greatest and least distance from point (2,1,-4) to ellipsoid x^2 +5y^2 +z^2 =1.

I tried solving it but i got a polynomial to power 4.

Its too long to post my working so ill just dropbox it.

dropboxcom/s/nobvp0739uk4yff/Photo%203-23-17%2C%2008%2004%2004.jpg?dl=0

dropboxcom/s/0xs6pyvht3nmrxo/Photo%203-23-17%2C%2008%2003%2052.jpg?dl=0

Answer 1

I worked it out, and also got a 4th-degree equation in x. So what? Just solve it for x using whatever method works best.

I did get z=x rather than z = -2x, but maybe I made a mistake.

Answer 2

Turns out my lecturer tells everyone theres no 5y^2... welp i just wasted few hrs...

I see... thanks for the help