Challenge problem:

Express the following algebraic quantities in terms of the variables λ,μ :

1)$\displaystyle a^2+b^2+c^2$

2)$\displaystyle a^3+b^3+c^3$

3)$\displaystyle a^5+b^5+c^5$

Where $\displaystyle a\neq b\neq c$ are the roots of the following equation:

$\displaystyle x^3+\lambda x+\mu=0$ ,$\displaystyle \lambda\neq 0,\mu\neq 0$ and real Nos

Moderator edit:Approved Challenge question.