Simplifying an expression $\frac{x^7+y^7+z^7}{xyz(x^4+y^4+z^4)}$ if we know $x+y+z=0$
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The following expression is given: $$\frac{x^7+y^7+z^7}{xyz(x^4+y^4+z^4)}$$
Simplify it, knowing that $x+y+z=0$.
algebra-precalculussymmetric-polynomials
asked 2012-03-02
user id:25981
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Use that $z=-(x+y)$ and substitute and suffer for a bit. I think you should get a nice answer :) – 2012-03-02
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@Victor: Diophantine equations? There is no equation and $x,y,z$ can be real/complex. contest-math? How do you know? I am removing those tags. – 2012-03-02