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If a + b + c = 0, then show that

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

    If a + b + c = 0, then show that
    6(a^5 + b^5 + c^5) = 5(a^3 + b^3 + c^3)(a^2 + b^2 + c^2)

    2. Relevant equations

    -

    3. The attempt at a solution
    Since a+b+c=0 then a^3 + b^3 + c^3=3abc .
    But then what? I've no idea , Please help.
     
  2. jcsd
  3. Jul 1, 2013 #2
    Im sorry to say, but none of these equations work, they are not equal so they have no solutions.

    I did a quick test by putting numbers in for a b and c. Being 2,3,4 the first part 6(a^5+b^5+c^5) = 5(a^3+b^3+c^3)(a^2+b^2+c^2) using the numbers i offered earlier. It comes to 7794=14355.

    The second equation comes to 99=72
     
  4. Jul 1, 2013 #3
    Please read the question carefully. It says that the above holds only if a+b+c=0 and that is what I want to prove.
     
  5. Jul 1, 2013 #4
    Well, that equation has quite a few solutions, wouldnt you need to solve for them all? Or does mater in the equations given below?
     
  6. Jul 1, 2013 #5
    I do not want to solve for solutions . ( By the way the solutions are all a , b and c that sum to 0) . But I want to prove that equation when a+b+c=0.
     
  7. Jul 1, 2013 #6
    I haven't tried this but the obvious thing would be to expand both sides and simplify by using the condition a + b + c = 0.
     
  8. Jul 1, 2013 #7
    No no, i mean, solve the other given equations using things like a+b=-c
     
  9. Jul 1, 2013 #8

    Ray Vickson

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    Put c = -a-b on both sides and expand both sides.
     
  10. Jul 1, 2013 #9
    Thanks a lot !
    After expanding I get LHS = -30 a^4 b-60 a^3 b^2-60 a^2 b^3-30 a b^4
    RHS= -30 a^4 b-60 a^3 b^2-60 a^2 b^3-30 a b^4
    LHS=RHS
    Q.E.D.
     
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