# Homework Help: Implicit Function Thm Application

1. Jul 6, 2012

### trap101

Investigate the possibility of solving x2-4x+2y2-yz = 1 for each of its variables in terms of the other two near the point (2,-1,3).

Attempt:

Ok so using the IFT I was able to determine that I can only slze for y,z. But in the question they ask me to solve for y and z. z was not problem, but y, they got a solution like this:

y = (z - [z2+8(1-x2+4x)]1/2) / 4

as well they said x = 2 (+ or -) [5-2y2+yz]1/2 and the square root vanishes at (y,z) = (-1,3) so there are two values of “ for some nearby values of and
and none for others.

Question: How did they solve for y? (What bloody algebra trick did they use that I'm not seeing? and how did those conditions on x appear?

2. Jul 6, 2012

### tiny-tim

hi trap101!
that's the standard -b ± √etc formula

3. Jul 6, 2012

### trap101

there are two values of x for some nearby values of y and z
and none for others.

Well after doing the mechanics for solving for y, I guess in that sort of scenario I should assume the other "variables" in this case x, z are just constants?

Last edited: Jul 6, 2012
4. Jul 7, 2012

yup!

5. Jul 7, 2012

### trap101

thnks again and won't be the last time, unless I get struck by lightning and all of a sudden I become a genius