1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding minimum for an equation with two variables

  1. Nov 6, 2013 #1
    1. The problem statement, all variables and given/known data

    I have the equation: x^2 + 2*x*y + 5*y^2 - 4*x - 6*y +7 and I have to find the minimum value
    I'm getting something that looks half like the correct answer, but not quite right...

    2. Relevant equations

    The answer from the answer book is:

    [x + 2*(y - 1)]^2 + (y + 1)^2 + 2

    3. The attempt at a solution

    Ok first I took 2*x*y and -4*x and turned them into 4*x*(y - 1), so I got:

    x^2 + 4*x*(y - 1) + 5*y^2 - 6*y + 7

    Then I turned x^2 + 4*x*(y - 1) into a square: [(x + 2*(y - 1)]^2 and subtracted [2*(y - 1)]^2, which is 4*(y - 1)^2 to balance it out, so I got:

    [x + 2*(y - 1)]^2 - 4*(y - 1)^2 + 5*y^2 - 6*y + 7

    However when I complete the square for the other part I get:

    [x + 2*(y - 1)]^2 - 4*(y - 1)^2 + 5*[(y - 3)^2 - 9] + 7

    when then gives me:

    [x + 2*(y - 1)]^2 - 4*(y - 1)^2 + 5*(y - 3)^2 - 38

    and this is not what the answer in the answer book I've written above is.Where did I go wrong?
     
  2. jcsd
  3. Nov 6, 2013 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    That doesn't look like a "minimum value" of anything. Please give the exact wording of the problem from your text.
     
  4. Nov 6, 2013 #3
    Here is the problem from the book(part (c) in the red rectangle):
    a3bd5adaf8a79c6b.png

    Here is the solution of (c) from the answer book(again surrounded in red):
    cd25dbf3ab519614.png
     
  5. Nov 6, 2013 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    ##2xy-4x\ne 4x(y-1)##
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding minimum for an equation with two variables
Loading...