# Homework Help: If a + b + c = 0, then show that

1. Jul 1, 2013

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

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3. The attempt at a solution
Since a+b+c=0 then a^3 + b^3 + c^3=3abc .

2. Jul 1, 2013

### Vacrin

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

3. Jul 1, 2013

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.

4. Jul 1, 2013

### Vacrin

Well, that equation has quite a few solutions, wouldnt you need to solve for them all? Or does mater in the equations given below?

5. Jul 1, 2013

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.

6. Jul 1, 2013

### Tsunoyukami

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.

7. Jul 1, 2013

### Vacrin

No no, i mean, solve the other given equations using things like a+b=-c

8. Jul 1, 2013

### Ray Vickson

Put c = -a-b on both sides and expand both sides.

9. Jul 1, 2013