Results 1 to 4 of 4

Math Help - [SOLVED] Planes of some sort?

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    8

    Exclamation [SOLVED] Planes of some sort?

    So in my calculus and vectors course, I was assigned the following question:

    Determine ALL real values of x, y and z, that satisfy the following
    system of equations:
    1)x^2 - yz + xy + zx = 82
    2)y^2 - zx + xy + yz = -18
    3)z^2 - xy + zx + yz = 18

    We have been learning about planes, so I am pretty sure I have to apply what I have learned about planes to this problem. But there are so many variables, and whatever I do (I've tried elimination and rearranging things) seems to lead me back to one of these equations! please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,570
    Thanks
    1428
    Quote Originally Posted by jenna0012 View Post
    So in my calculus and vectors course, I was assigned the following question:

    Determine ALL real values of x, y and z, that satisfy the following
    system of equations:
    1)x^2 - yz + xy + zx = 82
    2)y^2 - zx + xy + yz = -18
    3)z^2 - xy + zx + yz = 18

    We have been learning about planes, so I am pretty sure I have to apply what I have learned about planes to this problem. But there are so many variables, and whatever I do (I've tried elimination and rearranging things) seems to lead me back to one of these equations! please help
    Try completing the square on equation 3...

    z^2 + (x + y)z - xy = 18

    z^2 + (x + y)z + \left(\frac{x + y}{2}\right)^2 - \left(\frac{x + y}{2}\right)^2 - xy = 18

    \left(z + \frac{x + y}{2}\right)^2 - \left(\frac{x + y}{2}\right)^2 - xy = 18.


    Can you now solve for z and substitute these into the other equations to solve for x and y?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2009
    Posts
    8
    Quote Originally Posted by Prove It View Post
    Try completing the square on equation 3...

    z^2 + (x + y)z - xy = 18

    z^2 + (x + y)z + \left(\frac{x + y}{2}\right)^2 - \left(\frac{x + y}{2}\right)^2 - xy = 18

    \left(z + \frac{x + y}{2}\right)^2 - \left(\frac{x + y}{2}\right)^2 - xy = 18.


    Can you now solve for z and substitute these into the other equations to solve for x and y?
    hmm I see where you are going.. but I'm a bit confused at how you arrived at your third step
    \left(z + \frac{x + y}{2}\right)^2 - \left(\frac{x + y}{2}\right)^2 - xy = 18.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,570
    Thanks
    1428
    Quote Originally Posted by jenna0012 View Post
    hmm I see where you are going.. but I'm a bit confused at how you arrived at your third step
    \left(z + \frac{x + y}{2}\right)^2 - \left(\frac{x + y}{2}\right)^2 - xy = 18.
    It's a standard completing the square step...

    For a quadratic of the form x^2 + bx + c

    = x^2 + bx + \left(\frac{b}{2}\right)^2 - \left(\frac{b}{2}\right)^2 + c

    = \left(x + \frac{b}{2}\right)^2 - \left(\frac{b}{2}\right)^2 + c
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Planes and vectors please help
    Posted in the Geometry Forum
    Replies: 2
    Last Post: April 12th 2010, 02:43 PM
  2. [SOLVED] Distance between Parallel Planes
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 26th 2009, 04:12 PM
  3. Replies: 3
    Last Post: May 10th 2009, 09:53 AM
  4. [SOLVED] Planes & Archery
    Posted in the Geometry Forum
    Replies: 2
    Last Post: April 1st 2009, 11:40 AM
  5. [SOLVED] Projectile motion in inclined planes?
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: August 18th 2008, 08:29 PM

Search Tags


/mathhelpforum @mathhelpforum