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!

Math olympics problem

  1. Mar 6, 2010 #1
    1. The problem statement, all variables and given/known data
    I had this problem on the national math olympics of my country yesterday, I couldn't solve it... Knowing that the first statement is true, calculate the value of the second equation.


    2. Relevant equations
    [tex]\frac{a}{b+c+d}[/tex]+[tex]\frac{b}{c+d+a}[/tex]+[tex]\frac{c}{a+b+d}[/tex]+[tex]\frac{d}{a+b+c}[/tex]=1

    Calculate the value of

    [tex]\frac{a^2}{b+c+d}[/tex]+[tex]\frac{b^2}{c+d+a}[/tex]+[tex]\frac{c^2}{a+b+d}[/tex]+[tex]\frac{d^2}{a+b+c}[/tex]

    3. The attempt at a solution

    I lost a lot of time in this problem. I first tried to make one single, although huge, fraction of it, yet it didn't seem to simplify itself just to one value. Any better ways to approach this?




    By the way, please excuse me if I posted this on the wrong forum, I just found this website and am still getting used to it. Also, since it isn't my homework or something I have to eventually give as homework, it doesn't matter if you show me directly the answer... I just posted it on this forum because it somewhat looked like the right one.
     
    Last edited: Mar 6, 2010
  2. jcsd
  3. Mar 6, 2010 #2

    Mentallic

    User Avatar
    Homework Helper

    Caculate the following:

    [tex]\frac{a+b+c+d}{a+b+c+d}\left(\frac{a}{b+c+d}+\frac{b}{a+c+d}+\frac{c}{a+b+d}+\frac{d}{a+b+c}\right)=1[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Math olympics problem
  1. Math Problem (Replies: 6)

  2. Maths problem (Replies: 2)

  3. Math problems (Replies: 5)

  4. Math problem (Replies: 6)

  5. Math algebra problem (Replies: 13)

Loading...