1. Not finding help here? Sign up for a free 30min 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!

Show that x is a square expression

  1. Jun 16, 2011 #1
    1. The problem statement, all variables and given/known data
    n(n+3)(n+6)(n+9)=x-81
    Show that x is a squared expression


    2. Relevant equations
    These are some examples they give you:
    0*3*6*9=92-81
    1*4*7*10=192-81
    2*5*8*11=312-81


    3. The attempt at a solution
    To be honest, I have know idea where to start. So, I'd like a push in the right direction.
     
  2. jcsd
  3. Jun 16, 2011 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Shawn! :smile:

    You need to show that n(n+3)(n+6)(n+9) + 81 is a square …

    have you tried expanding it?​

    (alternatively, you could try finding a quadratic formula that fits 9,19,31 … :wink:)
     
  4. Jun 16, 2011 #3

    phinds

    User Avatar
    Gold Member
    2016 Award

    Very nice, Tiny-tim. I'm an old guy who remembers very little math but I love math problems, so try to work them out. This one had me flummoxed until I read your first hint and then after recovering from the headache caused by smacking myself in the forehead so hard I saw that it pretty much drops right out.
     
  5. Jun 16, 2011 #4

    phinds

    User Avatar
    Gold Member
    2016 Award

    Well, see, that's the problem with using a calculator. They keep you from learning how to THINK.
     
  6. Jun 16, 2011 #5

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Shawn, that's obviously wrong! :rolleyes:

    (how can it have a ".5" ?? :wink:)

    Try again! :smile:
     
  7. Jun 16, 2011 #6
    I just realized it's wrong, I deleted the reply. I expanded the expression, but I don't know where to go from there, I used a graphing calculator to graph the expression, it looks like a quadratic graph with the negative y-values mirrored over the x-axis, which makes sense cause the expression equals a square which is always positive.
     
  8. Jun 16, 2011 #7

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Shawn, it was nearly right …

    try expanding (n2 + 9n + c)2 :wink:
     
  9. Jun 16, 2011 #8
    That really helped, I have the answer now.

    ((x+4.5)2-11.25)2

    Thanks.
     
  10. Jun 16, 2011 #9

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    For future reference, the way to square-root a polynomial is to start from the left, and work your way across (a bit like long division) …

    for x4 + ax3 + bx2 + cx + d,

    https://www.physicsforums.com/library.php?do=view_item&itemid=107" for the x4 + ax3 part, and then add-on a unit to complete the square for the whole thing :wink:

    btw, my other hint was …

    9 19 31

    10 12

    2

    the 2 means it must be x2 + ax + b,

    subtracting 02 12 and 22 from 9 19 and 31 gives

    9 18 and 27, so a = b = 9 :biggrin:
     
    Last edited by a moderator: Apr 26, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Show that x is a square expression
  1. Expressing cos^6(x)? (Replies: 1)

Loading...