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Ratio proportion problem

  1. Jan 17, 2012 #1
    1. The problem statement, all variables and given/known data
    if(i have attached the equation's pic) then
    prove a=b=c or (a+b+c)(x+y+z)=ax+by+cz


    2. Relevant equations
    if a/b=c/d=e/f
    each ratio = (a+c+e)/(b+d+f)


    3. The attempt at a solution
    I was able to prove (a+b+c)(x+y+z)=ax+by+cz
    like this:
    each ratio= (a2+b2+c2-ab-bc-ca)/x+y+z
    also
    each ratio= (a3+b3+c[SUP3[/SUP]-3abc)/ax+by+cz
    (i hope i could make you understand how i did this)
    since
    (a2+b2+c2-ab-bc-ca)/x+y+z =(a3+b3+c[SUP3[/SUP]-3abc)/ax+by+cz
    →(a2+b2+c2-ab-bc-ca)/x+y+z=
    (a+b+c)(a2+b2+c2-ab-bc-ca)/ax+by+cz
    therefore
    (a+b+c)(x+y+z)=ax+by+cz
    fine uptill here but i can't understand how do i prove a=b=c??
    tried it like this
    (a+b+c)(x+y+z)=ax+by+cz
    →bx+cx+ay+cy+az+bz=0

    i can go further than this .Please give me a clue .
    And if i have gone wrong somewhere please point it out.
    Thank you.
     

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    Last edited: Jan 17, 2012
  2. jcsd
  3. Jan 17, 2012 #2

    SammyS

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    No picture is attached.
     
  4. Jan 18, 2012 #3

    HallsofIvy

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    Well, the picture is attached but there is no equation in it- just a sum of three expressions. What was this supposed to be equal to?
     
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